Disperso (optiko) - Vikipedio

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Havebla en 61 lingvo" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-61" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">61 lingvoj</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Dispersie_(optika)" title="Dispersie (optika) — afrikansa" lang="af" hreflang="af" data-title="Dispersie (optika)" data-language-autonym="Afrikaans" data-language-local-name="afrikansa" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%B4%D8%AA%D8%AA_(%D8%A8%D8%B5%D8%B1%D9%8A%D8%A7%D8%AA)" title="تشتت (بصريات) — araba" lang="ar" hreflang="ar" data-title="تشتت (بصريات)" data-language-autonym="العربية" data-language-local-name="araba" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Dispersi%C3%B3n_refractiva" title="Dispersión refractiva — asturia" lang="ast" hreflang="ast" data-title="Dispersión refractiva" data-language-autonym="Asturianu" data-language-local-name="asturia" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C4%B0%C5%9F%C4%B1%C4%9F%C4%B1n_dispersiyas%C4%B1" title="İşığın dispersiyası — azerbajĝana" lang="az" hreflang="az" data-title="İşığın dispersiyası" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajĝana" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%94%D1%8B%D1%81%D0%BF%D0%B5%D1%80%D1%81%D1%96%D1%8F_%D1%81%D0%B2%D1%8F%D1%82%D0%BB%D0%B0" title="Дысперсія святла — belorusa" lang="be" hreflang="be" data-title="Дысперсія святла" data-language-autonym="Беларуская" data-language-local-name="belorusa" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%94%D0%B8%D1%81%D0%BF%D0%B5%D1%80%D1%81%D0%B8%D1%8F_(%D0%BE%D0%BF%D1%82%D0%B8%D0%BA%D0%B0)" title="Дисперсия (оптика) — bulgara" lang="bg" hreflang="bg" data-title="Дисперсия (оптика)" data-language-autonym="Български" data-language-local-name="bulgara" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A6%BF%E0%A6%9A%E0%A7%8D%E0%A6%9B%E0%A7%81%E0%A6%B0%E0%A6%A3_(%E0%A6%86%E0%A6%B2%E0%A7%8B%E0%A6%95%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8)" title="বিচ্ছুরণ (আলোকবিজ্ঞান) — bengala" lang="bn" hreflang="bn" data-title="বিচ্ছুরণ (আলোকবিজ্ঞান)" data-language-autonym="বাংলা" data-language-local-name="bengala" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Dispersi%C3%B3_%C3%B2ptica" title="Dispersió òptica — kataluna" lang="ca" hreflang="ca" data-title="Dispersió òptica" data-language-autonym="Català" data-language-local-name="kataluna" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%BE%DB%95%DA%95%DB%95%D9%88%D8%A7%D8%B2%DB%95%DA%A9%D8%B1%D8%AF%D9%86" title="پەڕەوازەکردن — sorana" lang="ckb" hreflang="ckb" data-title="پەڕەوازەکردن" data-language-autonym="کوردی" data-language-local-name="sorana" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Disperze_(vln%C4%9Bn%C3%AD)" title="Disperze (vlnění) — ĉeĥa" lang="cs" hreflang="cs" data-title="Disperze (vlnění)" data-language-autonym="Čeština" data-language-local-name="ĉeĥa" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%C3%87%D1%83%D1%82%C4%83_%D1%81%D0%B0%D1%80%C4%83%D0%BC%C4%95" title="Çутă сарăмĕ — ĉuvaŝa" lang="cv" hreflang="cv" data-title="Çутă сарăмĕ" data-language-autonym="Чӑвашла" data-language-local-name="ĉuvaŝa" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Optisk_dispersion" title="Optisk dispersion — dana" lang="da" hreflang="da" data-title="Optisk dispersion" data-language-autonym="Dansk" data-language-local-name="dana" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%94%CE%B9%CE%B1%CF%83%CE%BA%CE%B5%CE%B4%CE%B1%CF%83%CE%BC%CF%8C%CF%82" title="Διασκεδασμός — greka" lang="el" hreflang="el" data-title="Διασκεδασμός" data-language-autonym="Ελληνικά" data-language-local-name="greka" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Dispersion_(optics)" title="Dispersion (optics) — angla" lang="en" hreflang="en" data-title="Dispersion (optics)" data-language-autonym="English" data-language-local-name="angla" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Dispersi%C3%B3n_refractiva" title="Dispersión refractiva — hispana" lang="es" hreflang="es" data-title="Dispersión refractiva" data-language-autonym="Español" data-language-local-name="hispana" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Dispersioon_(optika)" title="Dispersioon (optika) — estona" lang="et" hreflang="et" data-title="Dispersioon (optika)" data-language-autonym="Eesti" data-language-local-name="estona" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Sakabanaketa_optiko" title="Sakabanaketa optiko — eŭska" lang="eu" hreflang="eu" data-title="Sakabanaketa optiko" data-language-autonym="Euskara" data-language-local-name="eŭska" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%BE%D8%A7%D8%B4%D8%B4_(%D9%86%D9%88%D8%B1%D8%B4%D9%86%D8%A7%D8%B3%DB%8C)" title="پاشش (نورشناسی) — persa" lang="fa" hreflang="fa" data-title="پاشش (نورشناسی)" data-language-autonym="فارسی" data-language-local-name="persa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Dispersio" title="Dispersio — finna" lang="fi" hreflang="fi" data-title="Dispersio" data-language-autonym="Suomi" data-language-local-name="finna" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Dispersion_(m%C3%A9canique_ondulatoire)" title="Dispersion (mécanique ondulatoire) — franca" lang="fr" hreflang="fr" data-title="Dispersion (mécanique ondulatoire)" data-language-autonym="Français" data-language-local-name="franca" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Spr%C3%A9_(optaic)" title="Spré (optaic) — irlanda" lang="ga" hreflang="ga" data-title="Spré (optaic)" data-language-autonym="Gaeilge" data-language-local-name="irlanda" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A0%D7%A4%D7%99%D7%A6%D7%94" title="נפיצה — hebrea" lang="he" hreflang="he" data-title="נפיצה" data-language-autonym="עברית" data-language-local-name="hebrea" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A4%B0%E0%A4%BF%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%AA%E0%A4%A3" title="परिक्षेपण — hinda" lang="hi" hreflang="hi" data-title="परिक्षेपण" data-language-autonym="हिन्दी" data-language-local-name="hinda" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Disperzija_(optika)" title="Disperzija (optika) — kroata" lang="hr" hreflang="hr" data-title="Disperzija (optika)" data-language-autonym="Hrvatski" data-language-local-name="kroata" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Disp%C3%A8syon" title="Dispèsyon — haitia kreola" lang="ht" hreflang="ht" data-title="Dispèsyon" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitia kreola" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Diszperzi%C3%B3_(optika)" title="Diszperzió (optika) — hungara" lang="hu" hreflang="hu" data-title="Diszperzió (optika)" data-language-autonym="Magyar" data-language-local-name="hungara" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BC%D5%B8%D6%82%D5%B5%D5%BD%D5%AB_%D5%A4%D5%AB%D5%BD%D5%BA%D5%A5%D6%80%D5%BD%D5%AB%D5%A1" title="Լույսի դիսպերսիա — armena" lang="hy" hreflang="hy" data-title="Լույսի դիսպերսիա" data-language-autonym="Հայերեն" data-language-local-name="armena" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Dispersi" title="Dispersi — indonezia" lang="id" hreflang="id" data-title="Dispersi" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezia" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Dispersione_ottica" title="Dispersione ottica — itala" lang="it" hreflang="it" data-title="Dispersione ottica" data-language-autonym="Italiano" data-language-local-name="itala" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%88%86%E6%95%A3_(%E5%85%89%E5%AD%A6)" title="分散 (光学) — japana" lang="ja" hreflang="ja" data-title="分散 (光学)" data-language-autonym="日本語" data-language-local-name="japana" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A1%E1%83%98%E1%83%9C%E1%83%90%E1%83%97%E1%83%9A%E1%83%98%E1%83%A1_%E1%83%93%E1%83%98%E1%83%A1%E1%83%9E%E1%83%94%E1%83%A0%E1%83%A1%E1%83%98%E1%83%90" title="სინათლის დისპერსია — kartvela" lang="ka" hreflang="ka" data-title="სინათლის დისპერსია" data-language-autonym="ქართული" data-language-local-name="kartvela" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%96%D0%B0%D1%80%D1%8B%D2%9B_%D0%B4%D0%B8%D1%81%D0%BF%D0%B5%D1%80%D1%81%D0%B8%D1%8F%D1%81%D1%8B" title="Жарық дисперсиясы — kazaĥa" lang="kk" hreflang="kk" data-title="Жарық дисперсиясы" data-language-autonym="Қазақша" data-language-local-name="kazaĥa" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B6%84%EC%82%B0_(%EA%B4%91%ED%95%99)" title="분산 (광학) — korea" lang="ko" hreflang="ko" data-title="분산 (광학)" data-language-autonym="한국어" data-language-local-name="korea" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/%C5%A0viesos_dispersija" title="Šviesos dispersija — litova" lang="lt" hreflang="lt" data-title="Šviesos dispersija" data-language-autonym="Lietuvių" data-language-local-name="litova" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Dispersija_(optika)" title="Dispersija (optika) — latva" lang="lv" hreflang="lv" data-title="Dispersija (optika)" data-language-autonym="Latviešu" data-language-local-name="latva" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A0%D0%B0%D1%81%D0%B5%D1%98%D1%83%D0%B2%D0%B0%D1%9A%D0%B5_(%D0%BE%D0%BF%D1%82%D0%B8%D0%BA%D0%B0)" title="Расејување (оптика) — makedona" lang="mk" hreflang="mk" data-title="Расејување (оптика)" data-language-autonym="Македонски" data-language-local-name="makedona" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AA%E0%B5%8D%E0%B4%B0%E0%B4%95%E0%B4%BE%E0%B4%B6%E0%B4%AA%E0%B5%8D%E0%B4%B0%E0%B4%95%E0%B5%80%E0%B5%BC%E0%B4%A3%E0%B5%8D%E0%B4%A3%E0%B4%A8%E0%B4%82" title="പ്രകാശപ്രകീർണ്ണനം — malajalama" lang="ml" hreflang="ml" data-title="പ്രകാശപ്രകീർണ്ണനം" data-language-autonym="മലയാളം" data-language-local-name="malajalama" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Dispersie_(natuurkunde)" title="Dispersie (natuurkunde) — nederlanda" lang="nl" hreflang="nl" data-title="Dispersie (natuurkunde)" data-language-autonym="Nederlands" data-language-local-name="nederlanda" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Dispersjon_i_optikk" title="Dispersjon i optikk — novnorvega" lang="nn" hreflang="nn" data-title="Dispersjon i optikk" data-language-autonym="Norsk nynorsk" data-language-local-name="novnorvega" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Dispersjon_(optikk)" title="Dispersjon (optikk) — dannorvega" lang="nb" hreflang="nb" data-title="Dispersjon (optikk)" data-language-autonym="Norsk bokmål" data-language-local-name="dannorvega" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%96%E0%A8%BF%E0%A9%B0%E0%A8%A1%E0%A8%BE%E0%A8%85_(%E0%A8%AA%E0%A9%8D%E0%A8%B0%E0%A8%95%E0%A8%BE%E0%A8%B8%E0%A8%BC)" title="ਖਿੰਡਾਅ (ਪ੍ਰਕਾਸ਼) — panĝaba" lang="pa" hreflang="pa" data-title="ਖਿੰਡਾਅ (ਪ੍ਰਕਾਸ਼)" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="panĝaba" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Dyspersja_(optyka)" title="Dyspersja (optyka) — pola" lang="pl" hreflang="pl" data-title="Dyspersja (optyka)" data-language-autonym="Polski" data-language-local-name="pola" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Dispers%C3%A3o_(%C3%B3ptica)" title="Dispersão (óptica) — portugala" lang="pt" hreflang="pt" data-title="Dispersão (óptica)" data-language-autonym="Português" data-language-local-name="portugala" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Dispersia_luminii" title="Dispersia luminii — rumana" lang="ro" hreflang="ro" data-title="Dispersia luminii" data-language-autonym="Română" data-language-local-name="rumana" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%94%D0%B8%D1%81%D0%BF%D0%B5%D1%80%D1%81%D0%B8%D1%8F_%D1%81%D0%B2%D0%B5%D1%82%D0%B0" title="Дисперсия света — rusa" lang="ru" hreflang="ru" data-title="Дисперсия света" data-language-autonym="Русский" data-language-local-name="rusa" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Rasipanje_(optika)" title="Rasipanje (optika) — serbo-Kroata" lang="sh" hreflang="sh" data-title="Rasipanje (optika)" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-Kroata" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Dispersion" title="Dispersion — Simple English" lang="en-simple" hreflang="en-simple" data-title="Dispersion" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Disperzia_(elektromagnetick%C3%A9_%C5%BEiarenie)" title="Disperzia (elektromagnetické žiarenie) — slovaka" lang="sk" hreflang="sk" data-title="Disperzia (elektromagnetické žiarenie)" data-language-autonym="Slovenčina" data-language-local-name="slovaka" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Disperzija_(optika)" title="Disperzija (optika) — slovena" lang="sl" hreflang="sl" data-title="Disperzija (optika)" data-language-autonym="Slovenščina" data-language-local-name="slovena" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Dispersioni_i_drit%C3%ABs" title="Dispersioni i dritës — albana" lang="sq" hreflang="sq" data-title="Dispersioni i dritës" data-language-autonym="Shqip" data-language-local-name="albana" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%94%D0%B8%D1%81%D0%BF%D0%B5%D1%80%D0%B7%D0%B8%D1%98%D0%B0_(%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0)" title="Дисперзија (физика) — serba" lang="sr" hreflang="sr" data-title="Дисперзија (физика)" data-language-autonym="Српски / srpski" data-language-local-name="serba" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Dispersion" title="Dispersion — sveda" lang="sv" hreflang="sv" data-title="Dispersion" data-language-autonym="Svenska" data-language-local-name="sveda" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A8%E0%AE%BF%E0%AE%B1%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AE%BF%E0%AE%B0%E0%AE%BF%E0%AE%95%E0%AF%88" title="நிறப்பிரிகை — tamila" lang="ta" hreflang="ta" data-title="நிறப்பிரிகை" data-language-autonym="தமிழ்" data-language-local-name="tamila" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%81%E0%B8%A3%E0%B8%B0%E0%B8%88%E0%B8%B2%E0%B8%A2_(%E0%B8%97%E0%B8%B1%E0%B8%A8%E0%B8%99%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C)" title="การกระจาย (ทัศนศาสตร์) — taja" lang="th" hreflang="th" data-title="การกระจาย (ทัศนศาสตร์)" data-language-autonym="ไทย" data-language-local-name="taja" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Da%C4%9F%C4%B1lma" title="Dağılma — turka" lang="tr" hreflang="tr" data-title="Dağılma" data-language-autonym="Türkçe" data-language-local-name="turka" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%94%D0%B8%D1%81%D0%BF%D0%B5%D1%80%D1%81%D1%96%D1%8F_%D1%81%D0%B2%D1%96%D1%82%D0%BB%D0%B0" title="Дисперсія світла — ukraina" lang="uk" hreflang="uk" data-title="Дисперсія світла" data-language-autonym="Українська" data-language-local-name="ukraina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Yorug%CA%BBlik_dispersiyasi" title="Yorugʻlik dispersiyasi — uzbeka" lang="uz" hreflang="uz" data-title="Yorugʻlik dispersiyasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbeka" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/T%C3%A1n_s%E1%BA%AFc" title="Tán sắc — vjetnama" lang="vi" hreflang="vi" data-title="Tán sắc" data-language-autonym="Tiếng Việt" data-language-local-name="vjetnama" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%89%B2%E6%95%A3%EF%BC%88%E5%85%89%E5%AD%A6%EF%BC%89" title="色散（光学） — vua" lang="wuu" hreflang="wuu" data-title="色散（光学）" data-language-autonym="吴语" data-language-local-name="vua" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%89%B2%E6%95%A3_(%E5%85%89%E5%AD%B8)" title="色散 (光學) — ĉina" lang="zh" hreflang="zh" data-title="色散 (光學)" data-language-autonym="中文" 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id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="eo" dir="ltr"><p><i>Pri la aliaj sencoj de la vorto vidu apartigilon </i><a href="/wiki/Disperso" class="mw-disambig" title="Disperso">disperso</a><i>.</i> </p> <hr /> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Dosiero:Optical-dispersion.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Optical-dispersion.png/250px-Optical-dispersion.png" decoding="async" width="250" height="167" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Optical-dispersion.png/375px-Optical-dispersion.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/59/Optical-dispersion.png/500px-Optical-dispersion.png 2x" data-file-width="1200" data-file-height="800" /></a><figcaption>Disperso de blanka lumo trans <a href="/wiki/Prismo" title="Prismo">prismo</a>.</figcaption></figure> <p>En <a href="/wiki/Optiko" title="Optiko">optiko</a>, <b>disperso</b> <sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> estas malkomponiĝo de <a href="/wiki/Lumo" title="Lumo">lumo</a> laŭ <a href="/wiki/Koloro" title="Koloro">koloroj</a>. Rezulte el ne tro dika radio de blanka lumo fariĝas diverskolora bendo. En ĝia unua ekstremo videblas ruĝa koloro, poste oranĝkolora, flava, verda, blua kaj violkolora en la alia ekstremo. Ekster limoj de la videbla parto estas areoj de <a href="/wiki/Transru%C4%9Da_radiado" class="mw-redirect" title="Transruĝa radiado">transruĝa</a> lumo kaj <a href="/wiki/Transviola_radiado" class="mw-redirect" title="Transviola radiado">transviolkolora lumo</a>. </p><p>Disperso okazas kiam lumo trairas optikajn aparatojn, kie estas <a href="/wiki/Refrakto" title="Refrakto">refrakto</a> pro tio, ke <a href="/wiki/Indico_de_refrakto" class="mw-redirect" title="Indico de refrakto">indico de refrakto</a> de la refraktanta medio dependas de <a href="/wiki/Frekvenco" title="Frekvenco">frekvenco</a> (aŭ <a href="/wiki/Longo_de_ondo" class="mw-redirect" title="Longo de ondo">longo de ondo</a>) de la lumo. </p><p>Tia disperso estas kaŭzo de <a href="/wiki/Aberacio_(optiko)" title="Aberacio (optiko)">kolora aberacio</a> en <a href="/wiki/Objektivo" title="Objektivo">objektivoj</a> kaj <a href="/wiki/Lenso" class="mw-disambig" title="Lenso">lensoj</a>. Ĝi ankaŭ kaŭzas <a href="/wiki/%C4%88ielarko" title="Ĉielarko">ĉielarkojn</a> pro multaj akvogutetoj en <a href="/wiki/Humideco" title="Humideco">humidaj</a> <a href="/wiki/Atmosfero" title="Atmosfero">atmosferoj</a>. </p><p>Disperso okazas ankaŭ kiam lumo trairas <a href="/w/index.php?title=Difrakta_krado&action=edit&redlink=1" class="new" title="Difrakta krado (paĝo ne ekzistas)">difraktan kradon</a> aŭ estas re<a href="/wiki/Spegulo" title="Spegulo">spegulata</a> de ĝi. </p> <div class="mw-heading mw-heading2"><h2 id="Ĝeneraligita_formuliĝo_de_la_altaj_ordoj_de_disperso_-_Lah-Laguerre-optiko"><span id=".C4.9Ceneraligita_formuli.C4.9Do_de_la_altaj_ordoj_de_disperso_-_Lah-Laguerre-optiko"></span>Ĝeneraligita formuliĝo de la altaj ordoj de disperso - Lah-Laguerre-optiko</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Disperso_(optiko)&veaction=edit&section=1" title="Redakti sekcion: Ĝeneraligita formuliĝo de la altaj ordoj de disperso - Lah-Laguerre-optiko" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Disperso_(optiko)&action=edit&section=1" title="Redakti la fontkodo de la sekcio: Ĝeneraligita formuliĝo de la altaj ordoj de disperso - Lah-Laguerre-optiko"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La priskribo de la kromata disperso en perturba maniero tra Taylor-koeficientoj estas avantaĝa por optimumigaj problemoj kie la disperso de pluraj malsamaj sistemoj devas esti ekvilibra. Ekzemple, en pepa pulsaj laseramplifiloj, la pulsoj unue estas streĉitaj en tempo per brankardo por eviti optikan difekton. Tiam en la plifortiga procezo, la pulsoj akumuliĝas neeviteble lineara kaj nelinia fazo pasanta tra materialoj. Kaj laste, la pulsoj estas kunpremitaj en diversaj specoj de kompresoroj. Por nuligi iujn ajn restajn pli altajn ordojn en la amasigita fazo, kutime individuaj ordoj estas mezuritaj kaj ekvilibrigitaj. Tamen, por unuformaj sistemoj, tia perturba priskribo ofte ne estas necesa (t.e., disvastigo en ondgvidiloj). La disvastigordoj estis ĝeneraligitaj en komputile amika maniero, en la formo de Lah-Laguerre-specaj transformoj.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>La disvastigordoj estas difinitaj per la Taylor-vastigo de la fazo aŭ la ondovektoro. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{c}\varphi \mathrm {(} \omega \mathrm {)} =\varphi \left.\ \right|_{\omega _{0}}+\left.\ {\frac {\partial \varphi }{\partial \omega }}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)+{\frac {1}{2}}\left.\ {\frac {\partial ^{2}\varphi }{\partial \omega ^{2}}}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)^{2}\ +\ldots +{\frac {1}{p!}}\left.\ {\frac {\partial ^{p}\varphi }{\partial \omega ^{p}}}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)^{p}+\ldots \end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mi>φ</mi> <msub> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mtext> </mtext> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ω</mi> </mrow> </mfrac> </mrow> </mrow> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>ω</mi> <mo>−</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msub> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>φ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mrow> <mi>ω</mi> <mo>−</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mtext> </mtext> <mo>+</mo> <mo>…</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>p</mi> <mo>!</mo> </mrow> </mfrac> </mrow> <msub> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mi>φ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mrow> <mi>ω</mi> <mo>−</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mo>+</mo> <mo>…</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{c}\varphi \mathrm {(} \omega \mathrm {)} =\varphi \left.\ \right|_{\omega _{0}}+\left.\ {\frac {\partial \varphi }{\partial \omega }}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)+{\frac {1}{2}}\left.\ {\frac {\partial ^{2}\varphi }{\partial \omega ^{2}}}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)^{2}\ +\ldots +{\frac {1}{p!}}\left.\ {\frac {\partial ^{p}\varphi }{\partial \omega ^{p}}}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)^{p}+\ldots \end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61817f7b0d2a64834da7509e58af3942436d4a05" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:85.927ex; height:5.509ex;" alt="{\displaystyle {\begin{array}{c}\varphi \mathrm {(} \omega \mathrm {)} =\varphi \left.\ \right|_{\omega _{0}}+\left.\ {\frac {\partial \varphi }{\partial \omega }}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)+{\frac {1}{2}}\left.\ {\frac {\partial ^{2}\varphi }{\partial \omega ^{2}}}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)^{2}\ +\ldots +{\frac {1}{p!}}\left.\ {\frac {\partial ^{p}\varphi }{\partial \omega ^{p}}}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)^{p}+\ldots \end{array}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{c}k\mathrm {(} \omega \mathrm {)} =k\left.\ \right|_{\omega _{0}}+\left.\ {\frac {\partial k}{\partial \omega }}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)+{\frac {1}{2}}\left.\ {\frac {\partial ^{2}k}{\partial \omega ^{2}}}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)^{2}\ +\ldots +{\frac {1}{p!}}\left.\ {\frac {\partial ^{p}k}{\partial \omega ^{p}}}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)^{p}+\ldots \end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mi>k</mi> <msub> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mtext> </mtext> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>k</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ω</mi> </mrow> </mfrac> </mrow> </mrow> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>ω</mi> <mo>−</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msub> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>k</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mrow> <mi>ω</mi> <mo>−</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mtext> </mtext> <mo>+</mo> <mo>…</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>p</mi> <mo>!</mo> </mrow> </mfrac> </mrow> <msub> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mi>k</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mrow> <mi>ω</mi> <mo>−</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mo>+</mo> <mo>…</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{c}k\mathrm {(} \omega \mathrm {)} =k\left.\ \right|_{\omega _{0}}+\left.\ {\frac {\partial k}{\partial \omega }}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)+{\frac {1}{2}}\left.\ {\frac {\partial ^{2}k}{\partial \omega ^{2}}}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)^{2}\ +\ldots +{\frac {1}{p!}}\left.\ {\frac {\partial ^{p}k}{\partial \omega ^{p}}}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)^{p}+\ldots \end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e98623c3d3324fc0470b863b4a557cdaea6aa814" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.678ex; margin-bottom: -0.327ex; width:85.116ex; height:5.176ex;" alt="{\displaystyle {\begin{array}{c}k\mathrm {(} \omega \mathrm {)} =k\left.\ \right|_{\omega _{0}}+\left.\ {\frac {\partial k}{\partial \omega }}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)+{\frac {1}{2}}\left.\ {\frac {\partial ^{2}k}{\partial \omega ^{2}}}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)^{2}\ +\ldots +{\frac {1}{p!}}\left.\ {\frac {\partial ^{p}k}{\partial \omega ^{p}}}\right|_{\omega _{0}}\left(\omega -\omega _{0}\right)^{p}+\ldots \end{array}}}"></span> </p><p>La disvastigrilatoj por la ondaktoro <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k\mathrm {(} \omega \mathrm {)} ={\frac {\omega }{c}}n\mathrm {(} \omega \mathrm {)} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ω</mi> <mi>c</mi> </mfrac> </mrow> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k\mathrm {(} \omega \mathrm {)} ={\frac {\omega }{c}}n\mathrm {(} \omega \mathrm {)} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3cc0e58f83c907ba4b924800c404d807646446e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.497ex; height:4.676ex;" alt="{\displaystyle k\mathrm {(} \omega \mathrm {)} ={\frac {\omega }{c}}n\mathrm {(} \omega \mathrm {)} }"></span> kaj la fazo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi \mathrm {(} \omega \mathrm {)} ={\frac {\omega }{c}}{\it {OP}}\mathrm {(} \omega \mathrm {)} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ω</mi> <mi>c</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">O</mi> <mi class="MJX-tex-mathit" mathvariant="italic">P</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi \mathrm {(} \omega \mathrm {)} ={\frac {\omega }{c}}{\it {OP}}\mathrm {(} \omega \mathrm {)} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7969a83c9e576c3e846bac0a0471805f2045816" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.769ex; height:4.676ex;" alt="{\displaystyle \varphi \mathrm {(} \omega \mathrm {)} ={\frac {\omega }{c}}{\it {OP}}\mathrm {(} \omega \mathrm {)} }"></span> povas esti esprimita kiel: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{c}{\frac {{\partial }^{p}}{\partial {\omega }^{p}}}k\mathrm {(} \omega \mathrm {)} ={\frac {1}{c}}\left(p{\frac {{\partial }^{p-1}}{\partial {\omega }^{p-1}}}n\mathrm {(} \omega \mathrm {)} +\omega {\frac {{\partial }^{p}}{\partial {\omega }^{p}}}n\mathrm {(} \omega \mathrm {)} \right)\ \end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>c</mi> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>+</mo> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mtext> </mtext> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{c}{\frac {{\partial }^{p}}{\partial {\omega }^{p}}}k\mathrm {(} \omega \mathrm {)} ={\frac {1}{c}}\left(p{\frac {{\partial }^{p-1}}{\partial {\omega }^{p-1}}}n\mathrm {(} \omega \mathrm {)} +\omega {\frac {{\partial }^{p}}{\partial {\omega }^{p}}}n\mathrm {(} \omega \mathrm {)} \right)\ \end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/783fa20983efd6f324d010516d2e12644476ef78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:41.444ex; height:4.843ex;" alt="{\displaystyle {\begin{array}{c}{\frac {{\partial }^{p}}{\partial {\omega }^{p}}}k\mathrm {(} \omega \mathrm {)} ={\frac {1}{c}}\left(p{\frac {{\partial }^{p-1}}{\partial {\omega }^{p-1}}}n\mathrm {(} \omega \mathrm {)} +\omega {\frac {{\partial }^{p}}{\partial {\omega }^{p}}}n\mathrm {(} \omega \mathrm {)} \right)\ \end{array}}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{c}{\frac {{\partial }^{p}}{\partial {\omega }^{p}}}\varphi \mathrm {(} \omega \mathrm {)} ={\frac {1}{c}}\left(p{\frac {{\partial }^{p-1}}{\partial {\omega }^{p-1}}}{\it {OP}}\mathrm {(} \omega \mathrm {)} +\omega {\frac {{\partial }^{p}}{\partial {\omega }^{p}}}{\it {OP}}\mathrm {(} \omega \mathrm {)} \right)\end{array}}(1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>c</mi> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">O</mi> <mi class="MJX-tex-mathit" mathvariant="italic">P</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>+</mo> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">O</mi> <mi class="MJX-tex-mathit" mathvariant="italic">P</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{c}{\frac {{\partial }^{p}}{\partial {\omega }^{p}}}\varphi \mathrm {(} \omega \mathrm {)} ={\frac {1}{c}}\left(p{\frac {{\partial }^{p-1}}{\partial {\omega }^{p-1}}}{\it {OP}}\mathrm {(} \omega \mathrm {)} +\omega {\frac {{\partial }^{p}}{\partial {\omega }^{p}}}{\it {OP}}\mathrm {(} \omega \mathrm {)} \right)\end{array}}(1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/823cd5dc2a15cd26b4e3ca568595afed28b9703e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:47.684ex; height:4.843ex;" alt="{\displaystyle {\begin{array}{c}{\frac {{\partial }^{p}}{\partial {\omega }^{p}}}\varphi \mathrm {(} \omega \mathrm {)} ={\frac {1}{c}}\left(p{\frac {{\partial }^{p-1}}{\partial {\omega }^{p-1}}}{\it {OP}}\mathrm {(} \omega \mathrm {)} +\omega {\frac {{\partial }^{p}}{\partial {\omega }^{p}}}{\it {OP}}\mathrm {(} \omega \mathrm {)} \right)\end{array}}(1)}"></span> </p><p>La derivaĵoj de iu diferencigebla funkcio <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f\mathrm {(} \omega \mathrm {|} \lambda \mathrm {)} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f\mathrm {(} \omega \mathrm {|} \lambda \mathrm {)} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c27e6867acdfffdcf2fc4e74b9fe8c089ca60d1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.536ex; height:2.843ex;" alt="{\displaystyle f\mathrm {(} \omega \mathrm {|} \lambda \mathrm {)} }"></span> en la ondolongo aŭ la frekvenca spaco estas precizigitaj tra Lah transformo kiel: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\frac {\partial {p}}{\partial {\omega }^{p}}}f\mathrm {(} \omega \mathrm {)} ={}{\left(\mathrm {-} \mathrm {1} \right)}^{p}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{p}\sum \limits _{m={0}}^{p}{{\mathcal {A}}\mathrm {(} p,m\mathrm {)} {\lambda }^{m}{\frac {{\partial }^{m}}{\partial {\lambda }^{m}}}f\mathrm {(} \lambda \mathrm {)} }\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <munderover> <mo movablelimits="false">∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>p</mi> <mo>,</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\frac {\partial {p}}{\partial {\omega }^{p}}}f\mathrm {(} \omega \mathrm {)} ={}{\left(\mathrm {-} \mathrm {1} \right)}^{p}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{p}\sum \limits _{m={0}}^{p}{{\mathcal {A}}\mathrm {(} p,m\mathrm {)} {\lambda }^{m}{\frac {{\partial }^{m}}{\partial {\lambda }^{m}}}f\mathrm {(} \lambda \mathrm {)} }\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cf58dd45d815e34c2e716a9280c3520bbe9e730" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:48.805ex; height:6.176ex;" alt="{\displaystyle {\begin{array}{l}{\frac {\partial {p}}{\partial {\omega }^{p}}}f\mathrm {(} \omega \mathrm {)} ={}{\left(\mathrm {-} \mathrm {1} \right)}^{p}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{p}\sum \limits _{m={0}}^{p}{{\mathcal {A}}\mathrm {(} p,m\mathrm {)} {\lambda }^{m}{\frac {{\partial }^{m}}{\partial {\lambda }^{m}}}f\mathrm {(} \lambda \mathrm {)} }\end{array}}}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8fa4cba3a446de313920e16251756e27312b825" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:0.647ex; height:1.176ex;" alt="{\displaystyle ,}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{c}{\frac {{\partial }^{p}}{\partial {\lambda }^{p}}}f\mathrm {(} \lambda \mathrm {)} ={}{\left(\mathrm {-} \mathrm {1} \right)}^{p}{\left({\frac {\omega }{\mathrm {2} \pi c}}\right)}^{p}\sum \limits _{m={0}}^{p}{{\mathcal {A}}\mathrm {(} p,m\mathrm {)} {\omega }^{m}{\frac {{\partial }^{m}}{\partial {\omega }^{m}}}f\mathrm {(} \omega \mathrm {)} }\end{array}}(2)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ω</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <munderover> <mo movablelimits="false">∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>p</mi> <mo>,</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{c}{\frac {{\partial }^{p}}{\partial {\lambda }^{p}}}f\mathrm {(} \lambda \mathrm {)} ={}{\left(\mathrm {-} \mathrm {1} \right)}^{p}{\left({\frac {\omega }{\mathrm {2} \pi c}}\right)}^{p}\sum \limits _{m={0}}^{p}{{\mathcal {A}}\mathrm {(} p,m\mathrm {)} {\omega }^{m}{\frac {{\partial }^{m}}{\partial {\omega }^{m}}}f\mathrm {(} \omega \mathrm {)} }\end{array}}(2)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4771256e364e77043be78073177220dc8df65bdc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:51.867ex; height:6.176ex;" alt="{\displaystyle {\begin{array}{c}{\frac {{\partial }^{p}}{\partial {\lambda }^{p}}}f\mathrm {(} \lambda \mathrm {)} ={}{\left(\mathrm {-} \mathrm {1} \right)}^{p}{\left({\frac {\omega }{\mathrm {2} \pi c}}\right)}^{p}\sum \limits _{m={0}}^{p}{{\mathcal {A}}\mathrm {(} p,m\mathrm {)} {\omega }^{m}{\frac {{\partial }^{m}}{\partial {\omega }^{m}}}f\mathrm {(} \omega \mathrm {)} }\end{array}}(2)}"></span> </p><p>La matricaj elementoj de la transformo estas la Lah-koeficientoj: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}\mathrm {(} p,m\mathrm {)} ={\frac {p\mathrm {!} }{\left(p\mathrm {-} m\right)\mathrm {!} m\mathrm {!} }}{\frac {\mathrm {(} p\mathrm {-} \mathrm {1)!} }{\mathrm {(} m\mathrm {-} \mathrm {1)!} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>p</mi> <mo>,</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>!</mo> </mrow> </mrow> <mrow> <mrow> <mo>(</mo> <mrow> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mi>m</mi> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>!</mo> </mrow> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>!</mo> </mrow> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}\mathrm {(} p,m\mathrm {)} ={\frac {p\mathrm {!} }{\left(p\mathrm {-} m\right)\mathrm {!} m\mathrm {!} }}{\frac {\mathrm {(} p\mathrm {-} \mathrm {1)!} }{\mathrm {(} m\mathrm {-} \mathrm {1)!} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6787258ece1ac7e925f973a92e1620ffc4d387fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:30.743ex; height:6.509ex;" alt="{\displaystyle {\mathcal {A}}\mathrm {(} p,m\mathrm {)} ={\frac {p\mathrm {!} }{\left(p\mathrm {-} m\right)\mathrm {!} m\mathrm {!} }}{\frac {\mathrm {(} p\mathrm {-} \mathrm {1)!} }{\mathrm {(} m\mathrm {-} \mathrm {1)!} }}}"></span> </p><p>Skribita por la GDD ĉi-supra esprimo deklaras ke konstanto kun ondolongo GGD, havos nul pli altajn ordojn. La pli altaj ordoj taksitaj de la GDD estas: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{c}{\frac {{\partial }^{p}}{\partial {\omega }^{p}}}GDD\mathrm {(} \omega \mathrm {)} ={}{\left(\mathrm {-} \mathrm {1} \right)}^{p}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{p}\sum \limits _{m={0}}^{p}{{\mathcal {A}}\mathrm {(} p,m\mathrm {)} {\lambda }^{m}{\frac {{\partial }^{m}}{\partial {\lambda }^{m}}}GDD\mathrm {(} \lambda \mathrm {)} }\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>G</mi> <mi>D</mi> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <munderover> <mo movablelimits="false">∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>p</mi> <mo>,</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>G</mi> <mi>D</mi> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{c}{\frac {{\partial }^{p}}{\partial {\omega }^{p}}}GDD\mathrm {(} \omega \mathrm {)} ={}{\left(\mathrm {-} \mathrm {1} \right)}^{p}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{p}\sum \limits _{m={0}}^{p}{{\mathcal {A}}\mathrm {(} p,m\mathrm {)} {\lambda }^{m}{\frac {{\partial }^{m}}{\partial {\lambda }^{m}}}GDD\mathrm {(} \lambda \mathrm {)} }\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7dec3b43d6342f1217cb4fe8b815efdfa5a0e49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:57.598ex; height:6.176ex;" alt="{\displaystyle {\begin{array}{c}{\frac {{\partial }^{p}}{\partial {\omega }^{p}}}GDD\mathrm {(} \omega \mathrm {)} ={}{\left(\mathrm {-} \mathrm {1} \right)}^{p}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{p}\sum \limits _{m={0}}^{p}{{\mathcal {A}}\mathrm {(} p,m\mathrm {)} {\lambda }^{m}{\frac {{\partial }^{m}}{\partial {\lambda }^{m}}}GDD\mathrm {(} \lambda \mathrm {)} }\end{array}}}"></span> </p><p>Anstataŭigi ekvacion (2) esprimitan por la refrakta indekso <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> aŭ optika vojo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle OP}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle OP}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cdb46a90bdafeabc0a654bb9ad4067d5ce34e832" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.519ex; height:2.176ex;" alt="{\displaystyle OP}"></span> en ekvacion (1) rezultigas fermitformajn esprimojn por la disvastigordoj. Ĝenerale la orda disvastigo POD estas Laguerre-speca transformo de negativa ordo du: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle POD={\frac {d^{p}\varphi (\omega )}{d\omega ^{p}}}=(-1)^{p}({\frac {\lambda }{2\pi c}})^{(p-1)}\sum _{m=0}^{p}{\mathcal {B(p,m)}}(\lambda )^{m}{\frac {d^{m}OP(\lambda )}{d\lambda ^{m}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mi>O</mi> <mi>D</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mi>φ</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>d</mi> <msup> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mn>2</mn> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>p</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msup> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">B</mi> <mo class="MJX-tex-caligraphic" mathvariant="script" stretchy="false">(</mo> <mi class="MJX-tex-caligraphic" mathvariant="script">p</mi> <mo class="MJX-tex-caligraphic" mathvariant="script">,</mo> <mi class="MJX-tex-caligraphic" mathvariant="script">m</mi> <mo class="MJX-tex-caligraphic" mathvariant="script" stretchy="false">)</mo> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mi>O</mi> <mi>P</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>d</mi> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle POD={\frac {d^{p}\varphi (\omega )}{d\omega ^{p}}}=(-1)^{p}({\frac {\lambda }{2\pi c}})^{(p-1)}\sum _{m=0}^{p}{\mathcal {B(p,m)}}(\lambda )^{m}{\frac {d^{m}OP(\lambda )}{d\lambda ^{m}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf63c5c8f3872207850659e11b57d59a27b03ceb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:63.119ex; height:7.009ex;" alt="{\displaystyle POD={\frac {d^{p}\varphi (\omega )}{d\omega ^{p}}}=(-1)^{p}({\frac {\lambda }{2\pi c}})^{(p-1)}\sum _{m=0}^{p}{\mathcal {B(p,m)}}(\lambda )^{m}{\frac {d^{m}OP(\lambda )}{d\lambda ^{m}}}}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8fa4cba3a446de313920e16251756e27312b825" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:0.647ex; height:1.176ex;" alt="{\displaystyle ,}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle POD={\frac {d^{p}k(\omega )}{d\omega ^{p}}}=(-1)^{p}({\frac {\lambda }{2\pi c}})^{(p-1)}\sum _{m=0}^{p}{\mathcal {B(p,m)}}(\lambda )^{m}{\frac {d^{m}n(\lambda )}{d\lambda ^{m}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mi>O</mi> <mi>D</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mi>k</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>d</mi> <msup> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mn>2</mn> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>p</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msup> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">B</mi> <mo class="MJX-tex-caligraphic" mathvariant="script" stretchy="false">(</mo> <mi class="MJX-tex-caligraphic" mathvariant="script">p</mi> <mo class="MJX-tex-caligraphic" mathvariant="script">,</mo> <mi class="MJX-tex-caligraphic" mathvariant="script">m</mi> <mo class="MJX-tex-caligraphic" mathvariant="script" stretchy="false">)</mo> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mi>n</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>d</mi> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle POD={\frac {d^{p}k(\omega )}{d\omega ^{p}}}=(-1)^{p}({\frac {\lambda }{2\pi c}})^{(p-1)}\sum _{m=0}^{p}{\mathcal {B(p,m)}}(\lambda )^{m}{\frac {d^{m}n(\lambda )}{d\lambda ^{m}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0fe957b5a906040806fc4fa5ab57b98f97547fca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:60.686ex; height:7.009ex;" alt="{\displaystyle POD={\frac {d^{p}k(\omega )}{d\omega ^{p}}}=(-1)^{p}({\frac {\lambda }{2\pi c}})^{(p-1)}\sum _{m=0}^{p}{\mathcal {B(p,m)}}(\lambda )^{m}{\frac {d^{m}n(\lambda )}{d\lambda ^{m}}}}"></span> </p><p>La matricaj elementoj de la transformoj estas la sensignaj Laguerre-koeficientoj de ordo minus 2, kaj estas donitaj kiel: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {B}}\mathrm {(} p,m\mathrm {)} ={\frac {p\mathrm {!} }{\left(p\mathrm {-} m\right)\mathrm {!} m\mathrm {!} }}{\frac {\mathrm {(} p\mathrm {-} \mathrm {2)!} }{\mathrm {(} m\mathrm {-} \mathrm {2)!} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">B</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>p</mi> <mo>,</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>!</mo> </mrow> </mrow> <mrow> <mrow> <mo>(</mo> <mrow> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mi>m</mi> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>!</mo> </mrow> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>!</mo> </mrow> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {B}}\mathrm {(} p,m\mathrm {)} ={\frac {p\mathrm {!} }{\left(p\mathrm {-} m\right)\mathrm {!} m\mathrm {!} }}{\frac {\mathrm {(} p\mathrm {-} \mathrm {2)!} }{\mathrm {(} m\mathrm {-} \mathrm {2)!} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/763c876ca1ad6254ab1678269112158b34d65c35" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:30.383ex; height:6.509ex;" alt="{\displaystyle {\mathcal {B}}\mathrm {(} p,m\mathrm {)} ={\frac {p\mathrm {!} }{\left(p\mathrm {-} m\right)\mathrm {!} m\mathrm {!} }}{\frac {\mathrm {(} p\mathrm {-} \mathrm {2)!} }{\mathrm {(} m\mathrm {-} \mathrm {2)!} }}}"></span> </p><p>La unuaj dek disvastigordoj, eksplicite skribitaj por la ondovektoro, estas: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {GD}}}={\frac {\partial }{\partial \omega }}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(n\mathrm {(} \omega \mathrm {)} +\omega {\frac {\partial n\mathrm {(} \omega \mathrm {)} }{\partial \omega }}\right)={\frac {\mathrm {1} }{c}}\left(n\mathrm {(} \lambda \mathrm {)} -\lambda {\frac {\partial n\mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}\right)=v_{gr}^{\mathrm {-} \mathrm {1} }\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">G</mi> <mi class="MJX-tex-mathit" mathvariant="italic">D</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>ω</mi> </mrow> </mfrac> </mrow> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>+</mo> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ω</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>−</mo> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> <mi>r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </mrow> </msubsup> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\boldsymbol {\it {GD}}}={\frac {\partial }{\partial \omega }}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(n\mathrm {(} \omega \mathrm {)} +\omega {\frac {\partial n\mathrm {(} \omega \mathrm {)} }{\partial \omega }}\right)={\frac {\mathrm {1} }{c}}\left(n\mathrm {(} \lambda \mathrm {)} -\lambda {\frac {\partial n\mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}\right)=v_{gr}^{\mathrm {-} \mathrm {1} }\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d05992467bdbe506eace5789e85bc6a6274376d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.514ex; margin-bottom: -0.324ex; width:64.797ex; height:4.843ex;" alt="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {GD}}}={\frac {\partial }{\partial \omega }}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(n\mathrm {(} \omega \mathrm {)} +\omega {\frac {\partial n\mathrm {(} \omega \mathrm {)} }{\partial \omega }}\right)={\frac {\mathrm {1} }{c}}\left(n\mathrm {(} \lambda \mathrm {)} -\lambda {\frac {\partial n\mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}\right)=v_{gr}^{\mathrm {-} \mathrm {1} }\end{array}}}"></span> </p><p>La grupa refrakta indekso <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{g}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{g}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22fe2da32e6c5c5eb0a3afe639d5c7ba130ce84a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.416ex; height:2.343ex;" alt="{\displaystyle n_{g}}"></span> estas difinita kiel: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{g}=cv_{gr}^{\mathrm {-} \mathrm {1} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> <mo>=</mo> <mi>c</mi> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> <mi>r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{g}=cv_{gr}^{\mathrm {-} \mathrm {1} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85f62e9ddc61cd3d47f297b0489a51c454aaca45" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.982ex; height:3.343ex;" alt="{\displaystyle n_{g}=cv_{gr}^{\mathrm {-} \mathrm {1} }}"></span>. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {GDD}}}={\frac {{\partial }^{2}}{\partial {\omega }^{\mathrm {2} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {2} {\frac {\partial n\mathrm {(} \omega \mathrm {)} }{\partial \omega }}+\omega {\frac {{\partial }^{2}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {2} }}}\right)={\frac {\mathrm {1} }{c}}\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)\left({\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}\right)\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">G</mi> <mi class="MJX-tex-mathit" mathvariant="italic">D</mi> <mi class="MJX-tex-mathit" mathvariant="italic">D</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ω</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\boldsymbol {\it {GDD}}}={\frac {{\partial }^{2}}{\partial {\omega }^{\mathrm {2} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {2} {\frac {\partial n\mathrm {(} \omega \mathrm {)} }{\partial \omega }}+\omega {\frac {{\partial }^{2}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {2} }}}\right)={\frac {\mathrm {1} }{c}}\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)\left({\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}\right)\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b0b9d569034f63dd01bc3d17feb66e22f72ef70" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:65.512ex; height:6.176ex;" alt="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {GDD}}}={\frac {{\partial }^{2}}{\partial {\omega }^{\mathrm {2} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {2} {\frac {\partial n\mathrm {(} \omega \mathrm {)} }{\partial \omega }}+\omega {\frac {{\partial }^{2}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {2} }}}\right)={\frac {\mathrm {1} }{c}}\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)\left({\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}\right)\end{array}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {TOD}}}={\frac {{\partial }^{3}}{\partial {\omega }^{\mathrm {3} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {3} {\frac {{\partial }^{2}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {2} }}}+\omega {\frac {{\partial }^{3}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {3} }}}\right)={-}{\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {2} }{\Bigl (}\mathrm {3} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+{\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}{\Bigr )}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">T</mi> <mi class="MJX-tex-mathit" mathvariant="italic">O</mi> <mi class="MJX-tex-mathit" mathvariant="italic">D</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\boldsymbol {\it {TOD}}}={\frac {{\partial }^{3}}{\partial {\omega }^{\mathrm {3} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {3} {\frac {{\partial }^{2}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {2} }}}+\omega {\frac {{\partial }^{3}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {3} }}}\right)={-}{\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {2} }{\Bigl (}\mathrm {3} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+{\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}{\Bigr )}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df23c7ee30bf8c169dc9b0f70fba4e31a17f8d77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:79.951ex; height:6.176ex;" alt="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {TOD}}}={\frac {{\partial }^{3}}{\partial {\omega }^{\mathrm {3} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {3} {\frac {{\partial }^{2}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {2} }}}+\omega {\frac {{\partial }^{3}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {3} }}}\right)={-}{\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {2} }{\Bigl (}\mathrm {3} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+{\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}{\Bigr )}\end{array}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {FOD}}}={\frac {{\partial }^{4}}{\partial {\omega }^{\mathrm {4} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {4} {\frac {{\partial }^{3}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {3} }}}+\omega {\frac {{\partial }^{4}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {4} }}}\right)={\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {3} }{\Bigl (}\mathrm {12} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {8} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+{\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}{\Bigr )}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">F</mi> <mi class="MJX-tex-mathit" mathvariant="italic">O</mi> <mi class="MJX-tex-mathit" mathvariant="italic">D</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\boldsymbol {\it {FOD}}}={\frac {{\partial }^{4}}{\partial {\omega }^{\mathrm {4} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {4} {\frac {{\partial }^{3}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {3} }}}+\omega {\frac {{\partial }^{4}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {4} }}}\right)={\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {3} }{\Bigl (}\mathrm {12} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {8} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+{\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}{\Bigr )}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49a4f3c8735073921d6cf5420f1a9ee696ebe306" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:91.413ex; height:6.176ex;" alt="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {FOD}}}={\frac {{\partial }^{4}}{\partial {\omega }^{\mathrm {4} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {4} {\frac {{\partial }^{3}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {3} }}}+\omega {\frac {{\partial }^{4}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {4} }}}\right)={\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {3} }{\Bigl (}\mathrm {12} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {8} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+{\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}{\Bigr )}\end{array}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {FiOD}}}={\frac {{\partial }^{5}}{\partial {\omega }^{\mathrm {5} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {5} {\frac {{\partial }^{4}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {4} }}}+\omega {\frac {{\partial }^{5}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {5} }}}\right)={-}{\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {4} }{\Bigl (}\mathrm {60} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {60} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {15} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+{\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}{\Bigr )}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">F</mi> <mi class="MJX-tex-mathit" mathvariant="italic">i</mi> <mi class="MJX-tex-mathit" mathvariant="italic">O</mi> <mi class="MJX-tex-mathit" mathvariant="italic">D</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>60</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>60</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>15</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\boldsymbol {\it {FiOD}}}={\frac {{\partial }^{5}}{\partial {\omega }^{\mathrm {5} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {5} {\frac {{\partial }^{4}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {4} }}}+\omega {\frac {{\partial }^{5}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {5} }}}\right)={-}{\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {4} }{\Bigl (}\mathrm {60} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {60} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {15} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+{\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}{\Bigr )}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103029ba16c096f73decdbd1905a66bbcabb26c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:108.514ex; height:6.176ex;" alt="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {FiOD}}}={\frac {{\partial }^{5}}{\partial {\omega }^{\mathrm {5} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {5} {\frac {{\partial }^{4}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {4} }}}+\omega {\frac {{\partial }^{5}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {5} }}}\right)={-}{\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {4} }{\Bigl (}\mathrm {60} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {60} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {15} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+{\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}{\Bigr )}\end{array}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {SiOD}}}={\frac {{\partial }^{6}}{\partial {\omega }^{\mathrm {6} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {6} {\frac {{\partial }^{5}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {5} }}}+\omega {\frac {{\partial }^{6}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {6} }}}\right)={\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {5} }{\Bigl (}\mathrm {360} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {480} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {180} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {24} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+{\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}{\Bigr )}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">S</mi> <mi class="MJX-tex-mathit" mathvariant="italic">i</mi> <mi class="MJX-tex-mathit" mathvariant="italic">O</mi> <mi class="MJX-tex-mathit" mathvariant="italic">D</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>360</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>480</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>180</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>24</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\boldsymbol {\it {SiOD}}}={\frac {{\partial }^{6}}{\partial {\omega }^{\mathrm {6} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {6} {\frac {{\partial }^{5}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {5} }}}+\omega {\frac {{\partial }^{6}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {6} }}}\right)={\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {5} }{\Bigl (}\mathrm {360} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {480} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {180} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {24} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+{\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}{\Bigr )}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d682da5d1c6cf3347d75af379e63a1c0823ef9d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:123.398ex; height:6.176ex;" alt="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {SiOD}}}={\frac {{\partial }^{6}}{\partial {\omega }^{\mathrm {6} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {6} {\frac {{\partial }^{5}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {5} }}}+\omega {\frac {{\partial }^{6}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {6} }}}\right)={\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {5} }{\Bigl (}\mathrm {360} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {480} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {180} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {24} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+{\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}{\Bigr )}\end{array}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {SeOD}}}={\frac {{\partial }^{7}}{\partial {\omega }^{\mathrm {7} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {7} {\frac {{\partial }^{6}n\mathrm {(} \omega \mathrm {)} }{{\partial \omega }^{\mathrm {6} }}}+\omega {\frac {{\partial }^{7}n\mathrm {(} \omega \mathrm {)} }{{\partial \omega }^{\mathrm {7} }}}\right)={-}{\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {6} }{\Bigl (}\mathrm {2520} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {4200} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {2100} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {420} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {35} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+{\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}{\Bigr )}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">S</mi> <mi class="MJX-tex-mathit" mathvariant="italic">e</mi> <mi class="MJX-tex-mathit" mathvariant="italic">O</mi> <mi class="MJX-tex-mathit" mathvariant="italic">D</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2520</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>4200</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2100</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>420</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>35</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\boldsymbol {\it {SeOD}}}={\frac {{\partial }^{7}}{\partial {\omega }^{\mathrm {7} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {7} {\frac {{\partial }^{6}n\mathrm {(} \omega \mathrm {)} }{{\partial \omega }^{\mathrm {6} }}}+\omega {\frac {{\partial }^{7}n\mathrm {(} \omega \mathrm {)} }{{\partial \omega }^{\mathrm {7} }}}\right)={-}{\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {6} }{\Bigl (}\mathrm {2520} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {4200} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {2100} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {420} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {35} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+{\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}{\Bigr )}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c729b1df0fbf5a5179c4dc540f89a0421c6d04e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:143.627ex; height:6.176ex;" alt="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {SeOD}}}={\frac {{\partial }^{7}}{\partial {\omega }^{\mathrm {7} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {7} {\frac {{\partial }^{6}n\mathrm {(} \omega \mathrm {)} }{{\partial \omega }^{\mathrm {6} }}}+\omega {\frac {{\partial }^{7}n\mathrm {(} \omega \mathrm {)} }{{\partial \omega }^{\mathrm {7} }}}\right)={-}{\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {6} }{\Bigl (}\mathrm {2520} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {4200} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {2100} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {420} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {35} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+{\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}{\Bigr )}\end{array}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {EOD}}}={\frac {{\partial }^{8}}{\partial {\omega }^{\mathrm {8} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {8} {\frac {{\partial }^{7}n\mathrm {(} \omega \mathrm {)} }{{\partial \omega }^{\mathrm {7} }}}+\omega {\frac {{\partial }^{8}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {8} }}}\right)={\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {7} }{\Bigl (}\mathrm {20160} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {40320} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {25200} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {6720} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {840} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+\\+\mathrm {48} {\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}+{\lambda }^{\mathrm {8} }{\frac {{\partial }^{8}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {8} }}}{\Bigr )}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">E</mi> <mi class="MJX-tex-mathit" mathvariant="italic">O</mi> <mi class="MJX-tex-mathit" mathvariant="italic">D</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>20160</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>40320</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>25200</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>6720</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>840</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> </mtd> </mtr> <mtr> <mtd> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>48</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\boldsymbol {\it {EOD}}}={\frac {{\partial }^{8}}{\partial {\omega }^{\mathrm {8} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {8} {\frac {{\partial }^{7}n\mathrm {(} \omega \mathrm {)} }{{\partial \omega }^{\mathrm {7} }}}+\omega {\frac {{\partial }^{8}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {8} }}}\right)={\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {7} }{\Bigl (}\mathrm {20160} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {40320} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {25200} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {6720} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {840} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+\\+\mathrm {48} {\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}+{\lambda }^{\mathrm {8} }{\frac {{\partial }^{8}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {8} }}}{\Bigr )}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ecc5312925d7163e05bd9acec20c882a202269e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.171ex; width:136.16ex; height:11.509ex;" alt="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {EOD}}}={\frac {{\partial }^{8}}{\partial {\omega }^{\mathrm {8} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {8} {\frac {{\partial }^{7}n\mathrm {(} \omega \mathrm {)} }{{\partial \omega }^{\mathrm {7} }}}+\omega {\frac {{\partial }^{8}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {8} }}}\right)={\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {7} }{\Bigl (}\mathrm {20160} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {40320} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {25200} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {6720} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {840} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+\\+\mathrm {48} {\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}+{\lambda }^{\mathrm {8} }{\frac {{\partial }^{8}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {8} }}}{\Bigr )}\end{array}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {NOD}}}={\frac {{\partial }^{9}}{\partial {\omega }^{\mathrm {9} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {9} {\frac {{\partial }^{8}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {8} }}}+\omega {\frac {{\partial }^{9}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {9} }}}\right)={-}{\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {8} }{\Bigl (}\mathrm {181440} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {423360} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {317520} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {105840} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {17640} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+\\+\mathrm {1512} {\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}+\mathrm {63} {\lambda }^{\mathrm {8} }{\frac {{\partial }^{8}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {8} }}}+{\lambda }^{\mathrm {9} }{\frac {{\partial }^{9}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {9} }}}{\Bigr )}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">N</mi> <mi class="MJX-tex-mathit" mathvariant="italic">O</mi> <mi class="MJX-tex-mathit" mathvariant="italic">D</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>181440</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>423360</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>317520</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>105840</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>17640</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> </mtd> </mtr> <mtr> <mtd> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1512</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>63</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\boldsymbol {\it {NOD}}}={\frac {{\partial }^{9}}{\partial {\omega }^{\mathrm {9} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {9} {\frac {{\partial }^{8}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {8} }}}+\omega {\frac {{\partial }^{9}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {9} }}}\right)={-}{\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {8} }{\Bigl (}\mathrm {181440} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {423360} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {317520} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {105840} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {17640} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+\\+\mathrm {1512} {\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}+\mathrm {63} {\lambda }^{\mathrm {8} }{\frac {{\partial }^{8}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {8} }}}+{\lambda }^{\mathrm {9} }{\frac {{\partial }^{9}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {9} }}}{\Bigr )}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c929772ae6d906952c4a3a350c2e151e3661fa8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.171ex; width:146.257ex; height:11.509ex;" alt="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {NOD}}}={\frac {{\partial }^{9}}{\partial {\omega }^{\mathrm {9} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {9} {\frac {{\partial }^{8}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {8} }}}+\omega {\frac {{\partial }^{9}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {9} }}}\right)={-}{\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {8} }{\Bigl (}\mathrm {181440} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {423360} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {317520} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {105840} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {17640} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+\\+\mathrm {1512} {\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}+\mathrm {63} {\lambda }^{\mathrm {8} }{\frac {{\partial }^{8}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {8} }}}+{\lambda }^{\mathrm {9} }{\frac {{\partial }^{9}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {9} }}}{\Bigr )}\end{array}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {TeOD}}}={\frac {{\partial }^{10}}{\partial {\omega }^{\mathrm {10} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {10} {\frac {{\partial }^{9}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {9} }}}+\omega {\frac {{\partial }^{10}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {10} }}}\right)={\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {9} }{\Bigl (}\mathrm {1814400} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {4838400} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {4233600} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+{1693440}{\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\\+\mathrm {352800} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+\mathrm {40320} {\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}+\mathrm {2520} {\lambda }^{\mathrm {8} }{\frac {{\partial }^{8}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {8} }}}+\mathrm {80} {\lambda }^{\mathrm {9} }{\frac {{\partial }^{9}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {9} }}}+{\lambda }^{\mathrm {10} }{\frac {{\partial }^{10}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {10} }}}{\Bigr )}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">T</mi> <mi class="MJX-tex-mathit" mathvariant="italic">e</mi> <mi class="MJX-tex-mathit" mathvariant="italic">O</mi> <mi class="MJX-tex-mathit" mathvariant="italic">D</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mi>c</mi> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1814400</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>4838400</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>4233600</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1693440</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> </mtd> </mtr> <mtr> <mtd> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>352800</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>40320</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2520</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>80</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\boldsymbol {\it {TeOD}}}={\frac {{\partial }^{10}}{\partial {\omega }^{\mathrm {10} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {10} {\frac {{\partial }^{9}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {9} }}}+\omega {\frac {{\partial }^{10}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {10} }}}\right)={\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {9} }{\Bigl (}\mathrm {1814400} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {4838400} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {4233600} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+{1693440}{\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\\+\mathrm {352800} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+\mathrm {40320} {\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}+\mathrm {2520} {\lambda }^{\mathrm {8} }{\frac {{\partial }^{8}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {8} }}}+\mathrm {80} {\lambda }^{\mathrm {9} }{\frac {{\partial }^{9}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {9} }}}+{\lambda }^{\mathrm {10} }{\frac {{\partial }^{10}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {10} }}}{\Bigr )}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bea9098a20eca0bad36c78d9e0fc9d19752113d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.171ex; width:135.699ex; height:11.509ex;" alt="{\displaystyle {\begin{array}{l}{\boldsymbol {\it {TeOD}}}={\frac {{\partial }^{10}}{\partial {\omega }^{\mathrm {10} }}}k\mathrm {(} \omega \mathrm {)} ={\frac {\mathrm {1} }{c}}\left(\mathrm {10} {\frac {{\partial }^{9}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {9} }}}+\omega {\frac {{\partial }^{10}n\mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {10} }}}\right)={\frac {\mathrm {1} }{c}}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {9} }{\Bigl (}\mathrm {1814400} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {4838400} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {4233600} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+{1693440}{\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\\+\mathrm {352800} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+\mathrm {40320} {\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}+\mathrm {2520} {\lambda }^{\mathrm {8} }{\frac {{\partial }^{8}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {8} }}}+\mathrm {80} {\lambda }^{\mathrm {9} }{\frac {{\partial }^{9}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {9} }}}+{\lambda }^{\mathrm {10} }{\frac {{\partial }^{10}n\mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {10} }}}{\Bigr )}\end{array}}}"></span> </p><p>Eksplicite, skribita por la fazo \varphi , la unuaj dek dispersordoj povas esti esprimitaj kiel funkcio de ondolongo uzante la Lah-transformojn (ekvacio (2)) kiel: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\frac {\partial {p}}{\partial {\omega }^{p}}}f\mathrm {(} \omega \mathrm {)} ={}{\left(\mathrm {-} \mathrm {1} \right)}^{p}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{p}\sum \limits _{m={0}}^{p}{{\mathcal {A}}\mathrm {(} p,m\mathrm {)} {\lambda }^{m}{\frac {{\partial }^{m}}{\partial {\lambda }^{m}}}f\mathrm {(} \lambda \mathrm {)} }\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <munderover> <mo movablelimits="false">∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>p</mi> <mo>,</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\frac {\partial {p}}{\partial {\omega }^{p}}}f\mathrm {(} \omega \mathrm {)} ={}{\left(\mathrm {-} \mathrm {1} \right)}^{p}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{p}\sum \limits _{m={0}}^{p}{{\mathcal {A}}\mathrm {(} p,m\mathrm {)} {\lambda }^{m}{\frac {{\partial }^{m}}{\partial {\lambda }^{m}}}f\mathrm {(} \lambda \mathrm {)} }\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cf58dd45d815e34c2e716a9280c3520bbe9e730" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:48.805ex; height:6.176ex;" alt="{\displaystyle {\begin{array}{l}{\frac {\partial {p}}{\partial {\omega }^{p}}}f\mathrm {(} \omega \mathrm {)} ={}{\left(\mathrm {-} \mathrm {1} \right)}^{p}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{p}\sum \limits _{m={0}}^{p}{{\mathcal {A}}\mathrm {(} p,m\mathrm {)} {\lambda }^{m}{\frac {{\partial }^{m}}{\partial {\lambda }^{m}}}f\mathrm {(} \lambda \mathrm {)} }\end{array}}}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8fa4cba3a446de313920e16251756e27312b825" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:0.647ex; height:1.176ex;" alt="{\displaystyle ,}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{c}{\frac {{\partial }^{p}}{\partial {\lambda }^{p}}}f\mathrm {(} \lambda \mathrm {)} ={}{\left(\mathrm {-} \mathrm {1} \right)}^{p}{\left({\frac {\omega }{\mathrm {2} \pi c}}\right)}^{p}\sum \limits _{m={0}}^{p}{{\mathcal {A}}\mathrm {(} p,m\mathrm {)} {\omega }^{m}{\frac {{\partial }^{m}}{\partial {\omega }^{m}}}f\mathrm {(} \omega \mathrm {)} }\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ω</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <munderover> <mo movablelimits="false">∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>p</mi> <mo>,</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{c}{\frac {{\partial }^{p}}{\partial {\lambda }^{p}}}f\mathrm {(} \lambda \mathrm {)} ={}{\left(\mathrm {-} \mathrm {1} \right)}^{p}{\left({\frac {\omega }{\mathrm {2} \pi c}}\right)}^{p}\sum \limits _{m={0}}^{p}{{\mathcal {A}}\mathrm {(} p,m\mathrm {)} {\omega }^{m}{\frac {{\partial }^{m}}{\partial {\omega }^{m}}}f\mathrm {(} \omega \mathrm {)} }\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02ff5c079806dac954ec4949e51d830651b71038" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:48.895ex; height:6.176ex;" alt="{\displaystyle {\begin{array}{c}{\frac {{\partial }^{p}}{\partial {\lambda }^{p}}}f\mathrm {(} \lambda \mathrm {)} ={}{\left(\mathrm {-} \mathrm {1} \right)}^{p}{\left({\frac {\omega }{\mathrm {2} \pi c}}\right)}^{p}\sum \limits _{m={0}}^{p}{{\mathcal {A}}\mathrm {(} p,m\mathrm {)} {\omega }^{m}{\frac {{\partial }^{m}}{\partial {\omega }^{m}}}f\mathrm {(} \omega \mathrm {)} }\end{array}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\frac {\partial \varphi \mathrm {(} \omega \mathrm {)} }{\partial \omega }}={-}\left({\frac {\mathrm {2} \pi c}{{\omega }^{\mathrm {2} }}}\right){\frac {\partial \varphi \mathrm {(} \omega \mathrm {)} }{\partial \lambda }}={-}\left({\frac {{\lambda }^{\mathrm {2} }}{\mathrm {2} \pi c}}\right){\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ω</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\frac {\partial \varphi \mathrm {(} \omega \mathrm {)} }{\partial \omega }}={-}\left({\frac {\mathrm {2} \pi c}{{\omega }^{\mathrm {2} }}}\right){\frac {\partial \varphi \mathrm {(} \omega \mathrm {)} }{\partial \lambda }}={-}\left({\frac {{\lambda }^{\mathrm {2} }}{\mathrm {2} \pi c}}\right){\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7c51125b5b97f45b9f97a756ea7f3a4707d8b4e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.514ex; margin-bottom: -0.324ex; width:39.658ex; height:4.843ex;" alt="{\displaystyle {\begin{array}{l}{\frac {\partial \varphi \mathrm {(} \omega \mathrm {)} }{\partial \omega }}={-}\left({\frac {\mathrm {2} \pi c}{{\omega }^{\mathrm {2} }}}\right){\frac {\partial \varphi \mathrm {(} \omega \mathrm {)} }{\partial \lambda }}={-}\left({\frac {{\lambda }^{\mathrm {2} }}{\mathrm {2} \pi c}}\right){\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}\end{array}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\frac {{\partial }^{2}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {2} }}}={\frac {\partial }{\partial \omega }}\left({\frac {\partial \varphi \mathrm {(} \omega \mathrm {)} }{\partial \omega }}\right)={\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {2} }\left(\mathrm {2} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+{\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}\right)\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>ω</mi> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ω</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\frac {{\partial }^{2}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {2} }}}={\frac {\partial }{\partial \omega }}\left({\frac {\partial \varphi \mathrm {(} \omega \mathrm {)} }{\partial \omega }}\right)={\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {2} }\left(\mathrm {2} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+{\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}\right)\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af657b88b09d72a10c19ef1067d609a1af9cf3c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:53.769ex; height:6.176ex;" alt="{\displaystyle {\begin{array}{l}{\frac {{\partial }^{2}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {2} }}}={\frac {\partial }{\partial \omega }}\left({\frac {\partial \varphi \mathrm {(} \omega \mathrm {)} }{\partial \omega }}\right)={\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {2} }\left(\mathrm {2} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+{\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}\right)\end{array}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\frac {{\partial }^{3}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {3} }}}={-}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {3} }\left(\mathrm {6} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {6} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+{\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}\right)\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\frac {{\partial }^{3}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {3} }}}={-}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {3} }\left(\mathrm {6} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {6} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+{\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}\right)\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f19784832f1b9c757645d42317f817e38a703617" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:53.723ex; height:6.176ex;" alt="{\displaystyle {\begin{array}{l}{\frac {{\partial }^{3}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {3} }}}={-}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {3} }\left(\mathrm {6} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {6} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+{\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}\right)\end{array}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\frac {{\partial }^{4}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {4} }}}={\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {4} }{\Bigl (}\mathrm {24} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {36} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {12} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+{\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}{\Bigr )}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>24</mn> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>36</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\frac {{\partial }^{4}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {4} }}}={\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {4} }{\Bigl (}\mathrm {24} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {36} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {12} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+{\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}{\Bigr )}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19be8dcebb536b9ee104dda83d49de4b36e51947" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.751ex; margin-bottom: -0.254ex; width:66.712ex; height:5.176ex;" alt="{\displaystyle {\begin{array}{l}{\frac {{\partial }^{4}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {4} }}}={\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {4} }{\Bigl (}\mathrm {24} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {36} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {12} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+{\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}{\Bigr )}\end{array}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\frac {{\partial }^{\mathrm {5} }\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {5} }}}={-}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {5} }{\Bigl (}\mathrm {120} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {240} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {120} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {20} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+{\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}{\Bigr )}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>120</mn> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>240</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>120</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>20</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\frac {{\partial }^{\mathrm {5} }\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {5} }}}={-}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {5} }{\Bigl (}\mathrm {120} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {240} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {120} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {20} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+{\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}{\Bigr )}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7178ad65464fe34796940e6159d92ebb444a786b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:85.512ex; height:5.176ex;" alt="{\displaystyle {\begin{array}{l}{\frac {{\partial }^{\mathrm {5} }\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {5} }}}={-}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {5} }{\Bigl (}\mathrm {120} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {240} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {120} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {20} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+{\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}{\Bigr )}\end{array}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\frac {{\partial }^{6}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {6} }}}={\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {6} }{\Bigl (}\mathrm {720} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {1800} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {1200} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {300} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {30} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}\mathrm {\ +} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}{\Bigr )}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>720</mn> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1800</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1200</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>300</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>30</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext> </mtext> <mo>+</mo> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\frac {{\partial }^{6}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {6} }}}={\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {6} }{\Bigl (}\mathrm {720} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {1800} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {1200} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {300} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {30} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}\mathrm {\ +} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}{\Bigr )}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78e8e709a98ef6c250b3d63014d64c32e958ec5a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:100.245ex; height:5.176ex;" alt="{\displaystyle {\begin{array}{l}{\frac {{\partial }^{6}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {6} }}}={\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {6} }{\Bigl (}\mathrm {720} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {1800} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {1200} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {300} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {30} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}\mathrm {\ +} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}{\Bigr )}\end{array}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\frac {{\partial }^{7}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {7} }}}={-}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {7} }{\Bigl (}\mathrm {5040} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {15120} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {12600} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {4200} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {630} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {42} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+{\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}{\Bigr )}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5040</mn> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>15120</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>12600</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>4200</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>630</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>42</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\frac {{\partial }^{7}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {7} }}}={-}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {7} }{\Bigl (}\mathrm {5040} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {15120} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {12600} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {4200} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {630} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {42} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+{\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}{\Bigr )}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0419307a29f683917798e4ec76eb60d30fa5768d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:121.822ex; height:5.176ex;" alt="{\displaystyle {\begin{array}{l}{\frac {{\partial }^{7}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {7} }}}={-}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {7} }{\Bigl (}\mathrm {5040} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {15120} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {12600} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {4200} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {630} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {42} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+{\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}{\Bigr )}\end{array}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\frac {{\partial }^{8}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {8} }}}={\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {8} }{\Bigl (}\mathrm {40320} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {141120} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {141120} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {58800} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {11760} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {1176} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+\mathrm {56} {\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}+\\+{\lambda }^{\mathrm {8} }{\frac {\partial ^{8}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {8} }}}{\Bigr )}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>40320</mn> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>141120</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>141120</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>58800</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>11760</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1176</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>56</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> </mtd> </mtr> <mtr> <mtd> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\frac {{\partial }^{8}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {8} }}}={\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {8} }{\Bigl (}\mathrm {40320} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {141120} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {141120} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {58800} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {11760} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {1176} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+\mathrm {56} {\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}+\\+{\lambda }^{\mathrm {8} }{\frac {\partial ^{8}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {8} }}}{\Bigr )}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17e7725a0d68f279ad83beb55491dd1257f93097" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.459ex; margin-bottom: -0.212ex; width:132.059ex; height:10.509ex;" alt="{\displaystyle {\begin{array}{l}{\frac {{\partial }^{8}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {8} }}}={\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {8} }{\Bigl (}\mathrm {40320} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {141120} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {141120} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {58800} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {11760} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {1176} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+\mathrm {56} {\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}+\\+{\lambda }^{\mathrm {8} }{\frac {\partial ^{8}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {8} }}}{\Bigr )}\end{array}}}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\frac {{\partial }^{9}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {9} }}}={-}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {9} }{\Bigl (}\mathrm {362880} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {1451520} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {1693440} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {846720} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {211680} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {28224} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+\\+\mathrm {2016} {\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}+\mathrm {72} {\lambda }^{\mathrm {8} }{\frac {{\partial }^{8}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {8} }}}+{\lambda }^{\mathrm {9} }{\frac {\partial ^{\mathrm {9} }\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {9} }}}{\Bigr )}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>362880</mn> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1451520</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1693440</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>846720</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>211680</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>28224</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> </mtd> </mtr> <mtr> <mtd> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2016</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>72</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\frac {{\partial }^{9}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {9} }}}={-}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {9} }{\Bigl (}\mathrm {362880} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {1451520} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {1693440} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {846720} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {211680} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {28224} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+\\+\mathrm {2016} {\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}+\mathrm {72} {\lambda }^{\mathrm {8} }{\frac {{\partial }^{8}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {8} }}}+{\lambda }^{\mathrm {9} }{\frac {\partial ^{\mathrm {9} }\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {9} }}}{\Bigr )}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6b6caff9c03e57517751872c3edeca2a1d5f67e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.671ex; width:127.337ex; height:10.509ex;" alt="{\displaystyle {\begin{array}{l}{\frac {{\partial }^{9}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {9} }}}={-}{\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {9} }{\Bigl (}\mathrm {362880} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {1451520} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {1693440} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {846720} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {211680} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {28224} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+\\+\mathrm {2016} {\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}+\mathrm {72} {\lambda }^{\mathrm {8} }{\frac {{\partial }^{8}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {8} }}}+{\lambda }^{\mathrm {9} }{\frac {\partial ^{\mathrm {9} }\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {9} }}}{\Bigr )}\end{array}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{l}{\frac {{\partial }^{10}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {10} }}}={\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {10} }{\Bigl (}\mathrm {3628800} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {16329600} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {21772800} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {12700800} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {3810240} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {635040} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+\\+\mathrm {60480} {\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}+\mathrm {3240} {\lambda }^{\mathrm {8} }{\frac {{\partial }^{8}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {8} }}}+\mathrm {90} {\lambda }^{\mathrm {9} }{\frac {{\partial }^{9}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {9} }}}+{\lambda }^{\mathrm {10} }{\frac {{\partial }^{10}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {10} }}}{\Bigr )}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mi>π</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3628800</mn> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>16329600</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>21772800</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>12700800</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3810240</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>635040</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> </mtd> </mtr> <mtr> <mtd> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>60480</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3240</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>90</mn> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> </mrow> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{l}{\frac {{\partial }^{10}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {10} }}}={\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {10} }{\Bigl (}\mathrm {3628800} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {16329600} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {21772800} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {12700800} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {3810240} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {635040} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+\\+\mathrm {60480} {\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}+\mathrm {3240} {\lambda }^{\mathrm {8} }{\frac {{\partial }^{8}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {8} }}}+\mathrm {90} {\lambda }^{\mathrm {9} }{\frac {{\partial }^{9}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {9} }}}+{\lambda }^{\mathrm {10} }{\frac {{\partial }^{10}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {10} }}}{\Bigr )}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fb388107d29521af1cca4587be5684d9a627b42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.671ex; width:135.155ex; height:10.509ex;" alt="{\displaystyle {\begin{array}{l}{\frac {{\partial }^{10}\varphi \mathrm {(} \omega \mathrm {)} }{\partial {\omega }^{\mathrm {10} }}}={\left({\frac {\lambda }{\mathrm {2} \pi c}}\right)}^{\mathrm {10} }{\Bigl (}\mathrm {3628800} \lambda {\frac {\partial \varphi \mathrm {(} \lambda \mathrm {)} }{\partial \lambda }}+\mathrm {16329600} {\lambda }^{\mathrm {2} }{\frac {{\partial }^{2}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {2} }}}+\mathrm {21772800} {\lambda }^{\mathrm {3} }{\frac {{\partial }^{3}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {3} }}}+\mathrm {12700800} {\lambda }^{\mathrm {4} }{\frac {{\partial }^{4}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {4} }}}+\mathrm {3810240} {\lambda }^{\mathrm {5} }{\frac {{\partial }^{5}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {5} }}}+\mathrm {635040} {\lambda }^{\mathrm {6} }{\frac {{\partial }^{6}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {6} }}}+\\+\mathrm {60480} {\lambda }^{\mathrm {7} }{\frac {{\partial }^{7}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {7} }}}+\mathrm {3240} {\lambda }^{\mathrm {8} }{\frac {{\partial }^{8}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {8} }}}+\mathrm {90} {\lambda }^{\mathrm {9} }{\frac {{\partial }^{9}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {9} }}}+{\lambda }^{\mathrm {10} }{\frac {{\partial }^{10}\varphi \mathrm {(} \lambda \mathrm {)} }{\partial {\lambda }^{\mathrm {10} }}}{\Bigr )}\end{array}}}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Referencoj">Referencoj</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Disperso_(optiko)&veaction=edit&section=2" title="Redakti sekcion: Referencoj" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Disperso_(optiko)&action=edit&section=2" title="Redakti la fontkodo de la sekcio: Referencoj"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist references-small" style="padding-right: 6px;"> <ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">↑</a> <span class="reference-text"><a rel="nofollow" class="external free" href="https://www.reta-vortaro.de/revo/art/disper.html#disper.0o">https://www.reta-vortaro.de/revo/art/disper.html#disper.0o</a><a href="/wiki/ReVo" class="mw-redirect" title="ReVo">ReVo</a></span> </li> <li id="cite_note-2"><a href="#cite_ref-2">↑</a> <span class="reference-text"><cite style="font-style:normal;"> (2022-10-24) “Analytical Lah-Laguerre optical formalism for perturbative chromatic dispersion”, <i><a href="/w/index.php?title=Optics_Express&action=edit&redlink=1" class="new" title="Optics Express (paĝo ne ekzistas)">Optics Express</a></i> (EN) <b>30</b> (22), <span style="white-space:nowrap;">p. 40779–40808</span>. <a href="/wiki/Cifereca_objekta_identigilo" title="Cifereca objekta identigilo">doi</a>:<a href="//doi.org/10.1364/OE.457139" class="extiw" title="doi:10.1364/OE.457139">10.1364/OE.457139</a>. <a href="/wiki/Bibliografia_kodo" title="Bibliografia kodo">Bibkodo</a>:<a href="https://ui.adsabs.harvard.edu/abs/2022OExpr..3040779P/abstract" class="extiw" title="bibcode:2022OExpr..3040779P">2022OExpr..3040779P</a>.</cite><span style="display:none;"> </span> </span> </li> <li id="cite_note-3"><a href="#cite_ref-3">↑</a> <span class="reference-text"><cite style="font-style:normal;"> (2020-08-30) “Theory of the Chromatic Dispersion, Revisited” (EN). <a href="/wiki/ArXiv" title="ArXiv">arXiv</a>:<a href="https://arxiv.org/abs/2011.00066" class="extiw" title="arxiv:2011.00066">2011.00066</a>.</cite><span style="display:none;"> </span> </span> </li> </ol></div> <div class="noprint" id="aliaj_projektoj" style="float: right; clear: right; width: 250px; border: 1px solid #aaa; padding: 4px; font-size: 90%; background: #f9f9f9;"> <ul class="noarchive"><li class="commons"><span class="plainlinks"><a class="external text" 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Disperso (optiko) - Vikipedio