Euler-Mascheroni sabiti

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class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Kimliği alt bölümünü aç/kapa</span> </button> <ul id="toc-Kimliği-sublist" class="vector-toc-list"> <li id="toc-Gama_fonksiyonu_ile_ilişkisi" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Gama_fonksiyonu_ile_ilişkisi"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Gama fonksiyonu ile ilişkisi</span> </div> </a> <ul id="toc-Gama_fonksiyonu_ile_ilişkisi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zeta_fonksiyonu_ile_ilişkisi" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zeta_fonksiyonu_ile_ilişkisi"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Zeta fonksiyonu ile ilişkisi</span> </div> </a> <ul id="toc-Zeta_fonksiyonu_ile_ilişkisi-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Notlar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notlar"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Notlar</span> </div> </a> <ul id="toc-Notlar-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kaynakça" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kaynakça"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Kaynakça</span> </div> </a> <ul id="toc-Kaynakça-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dış_bağlantılar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dış_bağlantılar"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Dış bağlantılar</span> </div> </a> <ul id="toc-Dış_bağlantılar-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="İçindekiler" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="İçindekiler tablosunu değiştir" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">İçindekiler tablosunu değiştir</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Euler-Mascheroni sabiti</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Başka bir dildeki sayfaya gidin. 44 dilde mevcut" > <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-44" 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">44 dil</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AB%D8%A7%D8%A8%D8%AA_%D8%A3%D9%88%D9%8A%D9%84%D8%B1" title="ثابت أويلر - Arapça" lang="ar" hreflang="ar" data-title="ثابت أويلر" data-language-autonym="العربية" data-language-local-name="Arapça" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D0%B0%D1%81%D1%82%D0%B0%D1%8F%D0%BD%D0%BD%D0%B0%D1%8F_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80%D0%B0_%E2%80%94_%D0%9C%D0%B0%D1%81%D0%BA%D0%B5%D1%80%D0%BE%D0%BD%D1%96" title="Пастаянная Эйлера — Маскероні - Belarusça" lang="be" hreflang="be" data-title="Пастаянная Эйлера — Маскероні" data-language-autonym="Беларуская" data-language-local-name="Belarusça" 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%9A%D0%BE%D0%BD%D1%81%D1%82%D0%B0%D0%BD%D1%82%D0%B0_%D0%BD%D0%B0_%D0%9E%D0%B9%D0%BB%D0%B5%D1%80_%E2%80%93_%D0%9C%D0%B0%D1%81%D0%BA%D0%B5%D1%80%D0%BE%D0%BD%D0%B8" title="Константа на Ойлер – Маскерони - Bulgarca" lang="bg" hreflang="bg" data-title="Константа на Ойлер – Маскерони" data-language-autonym="Български" data-language-local-name="Bulgarca" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Constant_d%27Euler-Mascheroni" title="Constant d'Euler-Mascheroni - Katalanca" lang="ca" hreflang="ca" data-title="Constant d'Euler-Mascheroni" data-language-autonym="Català" data-language-local-name="Katalanca" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Eulerova_konstanta" title="Eulerova konstanta - Çekçe" lang="cs" hreflang="cs" data-title="Eulerova konstanta" data-language-autonym="Čeština" data-language-local-name="Çekçe" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Euler-Mascheroni-Konstante" title="Euler-Mascheroni-Konstante - Almanca" lang="de" hreflang="de" data-title="Euler-Mascheroni-Konstante" data-language-autonym="Deutsch" data-language-local-name="Almanca" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Euler%27s_constant" title="Euler's constant - İngilizce" lang="en" hreflang="en" data-title="Euler's constant" data-language-autonym="English" data-language-local-name="İngilizce" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Konstanto_de_E%C5%ADlero-Mascheroni" title="Konstanto de Eŭlero-Mascheroni - Esperanto" lang="eo" hreflang="eo" data-title="Konstanto de Eŭlero-Mascheroni" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Constante_de_Euler-Mascheroni" title="Constante de Euler-Mascheroni - İspanyolca" lang="es" hreflang="es" data-title="Constante de Euler-Mascheroni" data-language-autonym="Español" data-language-local-name="İspanyolca" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Euler-Mascheroni_konstante" title="Euler-Mascheroni konstante - Baskça" lang="eu" hreflang="eu" data-title="Euler-Mascheroni konstante" data-language-autonym="Euskara" data-language-local-name="Baskça" 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/%D8%AB%D8%A7%D8%A8%D8%AA_%D8%A7%D9%88%DB%8C%D9%84%D8%B1%E2%80%93%D9%85%D8%A7%D8%B3%DA%A9%D8%B1%D9%88%D9%86%DB%8C" title="ثابت اویلر–ماسکرونی - Farsça" lang="fa" hreflang="fa" data-title="ثابت اویلر–ماسکرونی" data-language-autonym="فارسی" data-language-local-name="Farsça" 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/Eulerin%E2%80%93Mascheronin_vakio" title="Eulerin–Mascheronin vakio - Fince" lang="fi" hreflang="fi" data-title="Eulerin–Mascheronin vakio" data-language-autonym="Suomi" data-language-local-name="Fince" 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/Constante_d%27Euler-Mascheroni" title="Constante d'Euler-Mascheroni - Fransızca" lang="fr" hreflang="fr" data-title="Constante d'Euler-Mascheroni" data-language-autonym="Français" data-language-local-name="Fransızca" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%91%D7%95%D7%A2_%D7%90%D7%95%D7%99%D7%9C%D7%A8-%D7%9E%D7%A1%D7%A7%D7%A8%D7%95%D7%A0%D7%99" title="קבוע אוילר-מסקרוני - İbranice" lang="he" hreflang="he" data-title="קבוע אוילר-מסקרוני" data-language-autonym="עברית" data-language-local-name="İbranice" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Eulerova_konstanta" title="Eulerova konstanta - Hırvatça" lang="hr" hreflang="hr" data-title="Eulerova konstanta" data-language-autonym="Hrvatski" data-language-local-name="Hırvatça" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Euler%E2%80%93Mascheroni-%C3%A1lland%C3%B3" title="Euler–Mascheroni-állandó - Macarca" lang="hu" hreflang="hu" data-title="Euler–Mascheroni-állandó" data-language-autonym="Magyar" data-language-local-name="Macarca" 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%B7%D5%B5%D5%AC%D5%A5%D6%80-%D5%84%D5%A1%D5%BD%D5%AF%D5%A5%D6%80%D5%B8%D5%B6%D5%AB_%D5%B0%D5%A1%D5%BD%D5%BF%D5%A1%D5%BF%D5%B8%D6%82%D5%B6" title="Էյլեր-Մասկերոնի հաստատուն - Ermenice" lang="hy" hreflang="hy" data-title="Էյլեր-Մասկերոնի հաստատուն" data-language-autonym="Հայերեն" data-language-local-name="Ermenice" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Constante_de_Euler-Mascheroni" title="Constante de Euler-Mascheroni - İnterlingua" lang="ia" hreflang="ia" data-title="Constante de Euler-Mascheroni" data-language-autonym="İnterlingua" data-language-local-name="İnterlingua" class="interlanguage-link-target"><span>İnterlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Konstanta_Euler%E2%80%93Mascheroni" title="Konstanta Euler–Mascheroni - Endonezce" lang="id" hreflang="id" data-title="Konstanta Euler–Mascheroni" data-language-autonym="Bahasa Indonesia" data-language-local-name="Endonezce" 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/Costante_di_Eulero-Mascheroni" title="Costante di Eulero-Mascheroni - İtalyanca" lang="it" hreflang="it" data-title="Costante di Eulero-Mascheroni" data-language-autonym="İtaliano" data-language-local-name="İtalyanca" class="interlanguage-link-target"><span>İtaliano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%AA%E3%82%A4%E3%83%A9%E3%83%BC%E3%81%AE%E5%AE%9A%E6%95%B0" title="オイラーの定数 - Japonca" lang="ja" hreflang="ja" data-title="オイラーの定数" data-language-autonym="日本語" data-language-local-name="Japonca" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%AD%D0%B9%D0%BB%D0%B5%D1%80_%E2%80%94_%D0%9C%D0%B0%D1%81%D0%BA%D0%B5%D1%80%D0%BE%D0%BD%D0%B8_%D1%82%D2%B1%D1%80%D0%B0%D2%9B%D1%82%D1%8B%D1%81%D1%8B" title="Эйлер — Маскерони тұрақтысы - Kazakça" lang="kk" hreflang="kk" data-title="Эйлер — Маскерони тұрақтысы" data-language-autonym="Қазақша" data-language-local-name="Kazakça" 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/%EC%98%A4%EC%9D%BC%EB%9F%AC-%EB%A7%88%EC%8A%A4%EC%BC%80%EB%A1%9C%EB%8B%88_%EC%83%81%EC%88%98" title="오일러-마스케로니 상수 - Korece" lang="ko" hreflang="ko" data-title="오일러-마스케로니 상수" data-language-autonym="한국어" data-language-local-name="Korece" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Custanta_da_Euler_Mascheroni" title="Custanta da Euler Mascheroni - Lombardça" lang="lmo" hreflang="lmo" data-title="Custanta da Euler Mascheroni" data-language-autonym="Lombard" data-language-local-name="Lombardça" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Oilerio-Maskeronio_konstanta" title="Oilerio-Maskeronio konstanta - Litvanca" lang="lt" hreflang="lt" data-title="Oilerio-Maskeronio konstanta" data-language-autonym="Lietuvių" data-language-local-name="Litvanca" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Constante_van_Euler-Mascheroni" title="Constante van Euler-Mascheroni - Felemenkçe" lang="nl" hreflang="nl" data-title="Constante van Euler-Mascheroni" data-language-autonym="Nederlands" data-language-local-name="Felemenkçe" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Euler-Mascheronis_konstant" title="Euler-Mascheronis konstant - Norveççe Bokmål" lang="nb" hreflang="nb" data-title="Euler-Mascheronis konstant" data-language-autonym="Norsk bokmål" data-language-local-name="Norveççe Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Sta%C5%82a_Eulera" title="Stała Eulera - Lehçe" lang="pl" hreflang="pl" data-title="Stała Eulera" data-language-autonym="Polski" data-language-local-name="Lehçe" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Costanta_d%27Euler" title="Costanta d'Euler - Piyemontece" lang="pms" hreflang="pms" data-title="Costanta d'Euler" data-language-autonym="Piemontèis" data-language-local-name="Piyemontece" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Constante_de_Euler-Mascheroni" title="Constante de Euler-Mascheroni - Portekizce" lang="pt" hreflang="pt" data-title="Constante de Euler-Mascheroni" data-language-autonym="Português" data-language-local-name="Portekizce" 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/Constanta_Euler%E2%80%93Mascheroni" title="Constanta Euler–Mascheroni - Rumence" lang="ro" hreflang="ro" data-title="Constanta Euler–Mascheroni" data-language-autonym="Română" data-language-local-name="Rumence" 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%9F%D0%BE%D1%81%D1%82%D0%BE%D1%8F%D0%BD%D0%BD%D0%B0%D1%8F_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80%D0%B0_%E2%80%94_%D0%9C%D0%B0%D1%81%D0%BA%D0%B5%D1%80%D0%BE%D0%BD%D0%B8" title="Постоянная Эйлера — Маскерони - Rusça" lang="ru" hreflang="ru" data-title="Постоянная Эйлера — Маскерони" data-language-autonym="Русский" data-language-local-name="Rusça" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Custanti_di_Euleru" title="Custanti di Euleru - Sicilyaca" lang="scn" hreflang="scn" data-title="Custanti di Euleru" data-language-autonym="Sicilianu" data-language-local-name="Sicilyaca" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant" title="Euler–Mascheroni constant - Simple English" lang="en-simple" hreflang="en-simple" data-title="Euler–Mascheroni constant" 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/Eulerova-Mascheroniova_kon%C5%A1tanta" title="Eulerova-Mascheroniova konštanta - Slovakça" lang="sk" hreflang="sk" data-title="Eulerova-Mascheroniova konštanta" data-language-autonym="Slovenčina" data-language-local-name="Slovakça" 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/Euler-Mascheronijeva_konstanta" title="Euler-Mascheronijeva konstanta - Slovence" lang="sl" hreflang="sl" data-title="Euler-Mascheronijeva konstanta" data-language-autonym="Slovenščina" data-language-local-name="Slovence" 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/Konstantja_e_Eulerit" title="Konstantja e Eulerit - Arnavutça" lang="sq" hreflang="sq" data-title="Konstantja e Eulerit" data-language-autonym="Shqip" data-language-local-name="Arnavutça" 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%9E%D1%98%D0%BB%D0%B5%D1%80-%D0%9C%D0%B0%D1%81%D0%BA%D0%B5%D1%80%D0%BE%D0%BD%D0%B8%D1%98%D0%B5%D0%B2%D0%B0_%D0%BA%D0%BE%D0%BD%D1%81%D1%82%D0%B0%D0%BD%D1%82%D0%B0" title="Ојлер-Маскеронијева константа - Sırpça" lang="sr" hreflang="sr" data-title="Ојлер-Маскеронијева константа" data-language-autonym="Српски / srpski" data-language-local-name="Sırpça" 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/Euler%E2%80%93Mascheronis_konstant" title="Euler–Mascheronis konstant - İsveççe" lang="sv" hreflang="sv" data-title="Euler–Mascheronis konstant" data-language-autonym="Svenska" data-language-local-name="İsveççe" 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%86%E0%AE%AF%E0%AF%8D%E0%AE%B2%E0%AE%B0%E0%AE%BF%E0%AE%A9%E0%AF%8D_%E0%AE%AE%E0%AE%BE%E0%AE%B1%E0%AE%BF%E0%AE%B2%E0%AE%BF" title="ஆய்லரின் மாறிலி - Tamilce" lang="ta" hreflang="ta" data-title="ஆய்லரின் மாறிலி" data-language-autonym="தமிழ்" data-language-local-name="Tamilce" 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mw-parser-output" lang="tr" dir="ltr"><div role="note" class="hatnote navigation-not-searchable">Başlığın diğer anlamları için <a href="/wiki/Euler_(anlam_ayr%C4%B1m%C4%B1)" class="mw-disambig" title="Euler (anlam ayrımı)">Euler (anlam ayrımı)</a> sayfasına bakınız.</div> <p><a href="/wiki/Matematiksel_analiz" class="mw-redirect" title="Matematiksel analiz">Matematiksel analizin</a> <a href="/wiki/Say%C4%B1_teorisi" class="mw-redirect" title="Sayı teorisi">sayı teorisinde</a> <b>Euler–Mascheroni sabiti</b> <a href="/wiki/Matematiksel_sabit" title="Matematiksel sabit">matematiksel sabit</a>'tir. Yunan harfi <a href="/wiki/Yunanca" title="Yunanca">Yunanca</a>: <span class="lang-el" lang="el" dir="ltr">γ</span> (<a href="/wiki/Gama" title="Gama">gama</a>) ile gösterilir. </p><p><a href="/wiki/Harmonik_seri" class="mw-redirect" title="Harmonik seri">Harmonik seri</a> ile <a href="/wiki/Do%C4%9Fal_logaritma" class="mw-redirect" title="Doğal logaritma">doğal logaritma</a> arasındaki fark veya <a href="/wiki/Dizinin_limiti" title="Dizinin limiti">limit</a>'tir. </p> <dl><dd><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 \gamma =\lim _{n\rightarrow \infty }\left(\sum _{k=1}^{n}{\frac {1}{k}}-\ln(n)\right)=\int _{1}^{\infty }\left({1 \over \lfloor x\rfloor }-{1 \over x}\right)\,dx.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow> <mo>(</mo> <mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>k</mi> </mfrac> </mrow> <mo>−</mo> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mo fence="false" stretchy="false">⌊</mo> <mi>x</mi> <mo fence="false" stretchy="false">⌋</mo> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma =\lim _{n\rightarrow \infty }\left(\sum _{k=1}^{n}{\frac {1}{k}}-\ln(n)\right)=\int _{1}^{\infty }\left({1 \over \lfloor x\rfloor }-{1 \over x}\right)\,dx.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c2518b06b8e40ac0f85fca5bf3fea976229b3f3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:50.925ex; height:7.509ex;" alt="{\displaystyle \gamma =\lim _{n\rightarrow \infty }\left(\sum _{k=1}^{n}{\frac {1}{k}}-\ln(n)\right)=\int _{1}^{\infty }\left({1 \over \lfloor x\rfloor }-{1 \over x}\right)\,dx.}"></span></dd></dl> <p>sayısal değerin 50 basamağı: </p> <dl><dd>0.57721 56649 01532 86060 65120 90082 40243 10421 59335 93992 …|</dd></dl> <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 \gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.262ex; height:2.176ex;" alt="{\displaystyle \gamma }"></span> ile <a href="/wiki/E_say%C4%B1s%C4%B1" title="E sayısı">e sayısı</a> karıştırılmamalıdır <i><a href="/wiki/E_say%C4%B1s%C4%B1" title="E sayısı">e</a></i> <i>Euler sayısı</i>, <a href="/wiki/Do%C4%9Fal_logaritma" class="mw-redirect" title="Doğal logaritma">doğal logaritma</a>'nın tabanı olarak bilinir. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Tarihçe"><span id="Tarih.C3.A7e"></span>Tarihçe</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Euler-Mascheroni_sabiti&veaction=edit&section=1" title="Değiştirilen bölüm: Tarihçe" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Euler-Mascheroni_sabiti&action=edit&section=1" title="Bölümün kaynak kodunu değiştir: Tarihçe"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sabit 1735'te <a href="/wiki/%C4%B0svi%C3%A7re" title="İsviçre">İsviçreli</a> matematikçi <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a>, <i>De Progressionibus harmonicis observationes</i> başlığı (Eneström Index 43) açıklanmıştır. Euler'in sabit için kullandığı notasyon <i>C</i> ve <i>O</i> dur. 1790'te, <a href="/wiki/%C4%B0talya" title="İtalya">İtalyan</a> matematikçi <a href="/w/index.php?title=Lorenzo_Mascheroni&action=edit&redlink=1" class="new" title="Lorenzo Mascheroni (sayfa mevcut değil)">Lorenzo Mascheroni</a>'nin sabit için kullandığı notasyon <i>A</i> ve <i>a</i> 'dır. γ gösterimine Euler veya Mascheroni sabiti dendi, daha sonra <a href="/wiki/Gama_fonksiyonu" title="Gama fonksiyonu">gama fonksiyonu</a> ile ilişkisi anlaşıldı. Mesela Carl Anton Bretschneider tarafından γ notasyonu 1835'te kullanıldı.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Tezahürleri"><span id="Tezah.C3.BCrleri"></span>Tezahürleri</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Euler-Mascheroni_sabiti&veaction=edit&section=2" title="Değiştirilen bölüm: Tezahürleri" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Euler-Mascheroni_sabiti&action=edit&section=2" title="Bölümün kaynak kodunu değiştir: Tezahürleri"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Euler-Mascheroni sabiti, diğer denklemler içerisinde görünür : </p> <ul><li><a href="/w/index.php?title=%C3%9Cstel_integral&action=edit&redlink=1" class="new" title="Üstel integral (sayfa mevcut değil)">üstel integral</a> ifadelerinde.</li> <li><a href="/wiki/Do%C4%9Fal_logaritma" class="mw-redirect" title="Doğal logaritma">doğal logaritma</a>'nın <a href="/wiki/Laplace_d%C3%B6n%C3%BC%C5%9F%C3%BCm%C3%BC" title="Laplace dönüşümü">Laplace dönüşümü</a>'nde.</li> <li><a href="/wiki/Riemann_zeta_fonksiyonu" class="mw-redirect" title="Riemann zeta fonksiyonu">Riemann zeta fonksiyonu</a>'nun Taylor serisine açılımında ilk terim, burada <a href="/w/index.php?title=Stieljes_sabiti&action=edit&redlink=1" class="new" title="Stieljes sabiti (sayfa mevcut değil)">Stieljes sabiti</a> ilk terimdir.</li> <li><a href="/wiki/Digama_fonksiyonu" title="Digama fonksiyonu">Digama fonksiyonu</a> hesaplamaları</li> <li><a href="/wiki/Gama_fonksiyonu" title="Gama fonksiyonu">Gama fonksiyonu</a>'ndan üretilen bir formül</li> <li><a href="/wiki/Euler_totient_fonksiyonu" class="mw-redirect" title="Euler totient fonksiyonu">Euler totient fonksiyonu</a> için bir eşitsizlik</li> <li><a href="/w/index.php?title=B%C3%B6len_fonksiyonu&action=edit&redlink=1" class="new" title="Bölen fonksiyonu (sayfa mevcut değil)">Bölen fonksiyonu</a>'nun büyük kesri</li> <li><a href="/w/index.php?title=Meissel-Mertens_sabiti&action=edit&redlink=1" class="new" title="Meissel-Mertens sabiti (sayfa mevcut değil)">Meissel-Mertens sabiti</a> için bir hesaplama</li> <li><a href="/w/index.php?title=Mertens%27in_%C3%BC%C3%A7%C3%BCnc%C3%BC_teoremi&action=edit&redlink=1" class="new" title="Mertens'in üçüncü teoremi (sayfa mevcut değil)">Mertens'in üçüncü teoremi</a></li> <li>ikinci tür <a href="/w/index.php?title=Bessel_denklemi&action=edit&redlink=1" class="new" title="Bessel denklemi (sayfa mevcut değil)">Bessel denklemi</a>'nin çözümü.</li> <li><a href="/wiki/Kuantum_alan_teorisi" title="Kuantum alan teorisi">Kuantum alan teorisi</a>'nde <a href="/w/index.php?title=Feynman_diagram&action=edit&redlink=1" class="new" title="Feynman diagram (sayfa mevcut değil)">Feynman diagram</a>'larının <a href="/w/index.php?title=Boyutsal_d%C3%BCzenlenmesinde&action=edit&redlink=1" class="new" title="Boyutsal düzenlenmesinde (sayfa mevcut değil)">Boyutsal düzenlenmesinde</a> .</li> <li><a href="/w/index.php?title=Gumbel_da%C4%9F%C4%B1l%C4%B1m%C4%B1n%C4%B1n_anlam%C4%B1&action=edit&redlink=1" class="new" title="Gumbel dağılımının anlamı (sayfa mevcut değil)">Gumbel dağılımının anlamı</a> ile.</li></ul> <p>Bu tür için daha fazla bilgi, bkz: <a rel="nofollow" class="external text" href="http://numbers.computation.free.fr/Constants/Gamma/gammaFormulas.html">Gourdon ve Sebah (2004).</a> 12 Aralık 2009 tarihinde <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> sitesinde <a rel="nofollow" class="external text" href="https://web.archive.org/web/20091212002936/http://numbers.computation.free.fr/Constants/Gamma/gammaFormulas.html">arşivlendi</a>. rmulas.html Gourdon and Sebah (2004).] </p> <div class="mw-heading mw-heading2"><h2 id="Kimliği"><span id="Kimli.C4.9Fi"></span>Kimliği</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Euler-Mascheroni_sabiti&veaction=edit&section=3" title="Değiştirilen bölüm: Kimliği" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Euler-Mascheroni_sabiti&action=edit&section=3" title="Bölümün kaynak kodunu değiştir: Kimliği"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>γ sayısının <a href="/w/index.php?title=Algebraic_number&action=edit&redlink=1" class="new" title="Algebraic number (sayfa mevcut değil)">cebirsel sayı</a> veya <a href="/w/index.php?title=Transcendental_number&action=edit&redlink=1" class="new" title="Transcendental number (sayfa mevcut değil)">aşkın sayı</a> olup olmadığı bilinmiyor. Hatta γ'nın <a href="/w/index.php?title=%C4%B0rrational_number&action=edit&redlink=1" class="new" title="İrrational number (sayfa mevcut değil)">irrasyonel sayı</a> olup olmadığıda bilinmiyor <a href="/w/index.php?title=S%C3%BCrekli_kesir&action=edit&redlink=1" class="new" title="Sürekli kesir (sayfa mevcut değil)">sürekli kesir</a>'le <a href="/w/index.php?title=Rational_number&action=edit&redlink=1" class="new" title="Rational number (sayfa mevcut değil)">rasyonel</a>, γ paydası 10<sup>242080</sup> 'dan büyük olmalıdır.<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Vikipedi:Kaynak_g%C3%B6sterme" title="Vikipedi:Kaynak gösterme"><span title="">kaynak belirtilmeli</span></a></i>]</sup> Birçok denklemde ortaya çıkan γ'nın (pi/2e~0.5778) irrasyonalitesi? büyük bir açık sorudur.Sondow'a bakınız (2003a). </p><p>Daha fazla bilgi için bakınız: <a rel="nofollow" class="external text" href="http://numbers.computation.free.fr/Constants/Gamma/gammaFormulas.html">Gourdon and Sebah (2002).</a> 12 Aralık 2009 tarihinde <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> sitesinde <a rel="nofollow" class="external text" href="https://web.archive.org/web/20091212002936/http://numbers.computation.free.fr/Constants/Gamma/gammaFormulas.html">arşivlendi</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Gama_fonksiyonu_ile_ilişkisi"><span id="Gama_fonksiyonu_ile_ili.C5.9Fkisi"></span>Gama fonksiyonu ile ilişkisi</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Euler-Mascheroni_sabiti&veaction=edit&section=4" title="Değiştirilen bölüm: Gama fonksiyonu ile ilişkisi" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Euler-Mascheroni_sabiti&action=edit&section=4" title="Bölümün kaynak kodunu değiştir: Gama fonksiyonu ile ilişkisi"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>γ <a href="/wiki/Digama_fonksiyonu" title="Digama fonksiyonu">digama fonksiyonu</a> Ψ ile ilişkilidir, Ψ,<a href="/wiki/Gama_fonksiyonu" title="Gama fonksiyonu">gama fonksiyonu</a> yani Γ 'unun türevidir.: </p> <dl><dd><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 \ -\gamma =\Gamma '(1)=\Psi (1).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo>−</mo> <mi>γ</mi> <mo>=</mo> <msup> <mi mathvariant="normal">Γ</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mi mathvariant="normal">Ψ</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ -\gamma =\Gamma '(1)=\Psi (1).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8bd08df693d77e285f9a189656fb0994635b178" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.416ex; height:3.009ex;" alt="{\displaystyle \ -\gamma =\Gamma '(1)=\Psi (1).}"></span></dd></dl> <p>Bunun limiti: </p> <dl><dd><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 -\gamma =\lim _{z\to 0}\left\{\Gamma (z)-{\frac {1}{z}}\right\}=\lim _{z\to 0}\left\{\Psi (z)+{\frac {1}{z}}\right\}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi>γ</mi> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow> <mo>{</mo> <mrow> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>z</mi> </mfrac> </mrow> </mrow> <mo>}</mo> </mrow> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow> <mo>{</mo> <mrow> <mi mathvariant="normal">Ψ</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>z</mi> </mfrac> </mrow> </mrow> <mo>}</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\gamma =\lim _{z\to 0}\left\{\Gamma (z)-{\frac {1}{z}}\right\}=\lim _{z\to 0}\left\{\Psi (z)+{\frac {1}{z}}\right\}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9b99586ffc3cb6f14b4b67b8c81137b4a9aeba2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:43.251ex; height:6.176ex;" alt="{\displaystyle -\gamma =\lim _{z\to 0}\left\{\Gamma (z)-{\frac {1}{z}}\right\}=\lim _{z\to 0}\left\{\Psi (z)+{\frac {1}{z}}\right\}.}"></span></dd></dl> <p>Daha öte limit sonuçları (Krämer, 2005): </p> <dl><dd><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 \lim _{z\to 0}{\frac {1}{z}}\left\{{\frac {1}{\Gamma (1+z)}}-{\frac {1}{\Gamma (1-z)}}\right\}=2\gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>z</mi> </mfrac> </mrow> <mrow> <mo>{</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mrow> <mo>}</mo> </mrow> <mo>=</mo> <mn>2</mn> <mi>γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{z\to 0}{\frac {1}{z}}\left\{{\frac {1}{\Gamma (1+z)}}-{\frac {1}{\Gamma (1-z)}}\right\}=2\gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a653df6825d891c48f4dd8b596ca59aa7bc95658" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:36.236ex; height:6.343ex;" alt="{\displaystyle \lim _{z\to 0}{\frac {1}{z}}\left\{{\frac {1}{\Gamma (1+z)}}-{\frac {1}{\Gamma (1-z)}}\right\}=2\gamma }"></span></dd> <dd><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 \lim _{z\to 0}{\frac {1}{z}}\left\{{\frac {1}{\Psi (1-z)}}-{\frac {1}{\Psi (1+z)}}\right\}={\frac {\pi ^{2}}{3\gamma ^{2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>z</mi> </mfrac> </mrow> <mrow> <mo>{</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi mathvariant="normal">Ψ</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi mathvariant="normal">Ψ</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mrow> <mo>}</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>3</mn> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{z\to 0}{\frac {1}{z}}\left\{{\frac {1}{\Psi (1-z)}}-{\frac {1}{\Psi (1+z)}}\right\}={\frac {\pi ^{2}}{3\gamma ^{2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b816ddabe68db0df43d585c3aebaf957f9c4ab0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:39.501ex; height:6.509ex;" alt="{\displaystyle \lim _{z\to 0}{\frac {1}{z}}\left\{{\frac {1}{\Psi (1-z)}}-{\frac {1}{\Psi (1+z)}}\right\}={\frac {\pi ^{2}}{3\gamma ^{2}}}.}"></span></dd></dl> <p><a href="/wiki/Beta_fonksiyonu" title="Beta fonksiyonu">beta fonksiyonu</a> ile ilişkisi (dolayısıyla <a href="/wiki/Gama_fonksiyonu" title="Gama fonksiyonu">gama fonksiyonu</a>) </p> <dl><dd><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 \gamma =\lim _{n\to \infty }\left\{{\frac {\Gamma ({\frac {1}{n}})\Gamma (n+1)\,n^{1+1/n}}{\Gamma (2+n+{\frac {1}{n}})}}-{\frac {n^{2}}{n+1}}\right\}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow> <mo>{</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mrow> <mo stretchy="false">)</mo> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>+</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>n</mi> </mrow> </msup> </mrow> <mrow> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo>+</mo> <mi>n</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mrow> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </mrow> <mo>}</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma =\lim _{n\to \infty }\left\{{\frac {\Gamma ({\frac {1}{n}})\Gamma (n+1)\,n^{1+1/n}}{\Gamma (2+n+{\frac {1}{n}})}}-{\frac {n^{2}}{n+1}}\right\}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb49e1e2efe9030f333bf8a0b9f003c05e3db88b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:44.2ex; height:7.509ex;" alt="{\displaystyle \gamma =\lim _{n\to \infty }\left\{{\frac {\Gamma ({\frac {1}{n}})\Gamma (n+1)\,n^{1+1/n}}{\Gamma (2+n+{\frac {1}{n}})}}-{\frac {n^{2}}{n+1}}\right\}.}"></span></dd></dl> <dl><dd><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 \gamma =\lim \limits _{m\to \infty }\sum _{k=1}^{m}{m \choose k}{\frac {(-1)^{k}}{k}}\ln(\Gamma (k+1)).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mo>=</mo> <munder> <mo form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mi>m</mi> <mi>k</mi> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> </mrow> <mi>k</mi> </mfrac> </mrow> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma =\lim \limits _{m\to \infty }\sum _{k=1}^{m}{m \choose k}{\frac {(-1)^{k}}{k}}\ln(\Gamma (k+1)).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/928e111232675bfa91f7641acf613cd598c14ac5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:38.644ex; height:7.009ex;" alt="{\displaystyle \gamma =\lim \limits _{m\to \infty }\sum _{k=1}^{m}{m \choose k}{\frac {(-1)^{k}}{k}}\ln(\Gamma (k+1)).}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Zeta_fonksiyonu_ile_ilişkisi"><span id="Zeta_fonksiyonu_ile_ili.C5.9Fkisi"></span>Zeta fonksiyonu ile ilişkisi</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Euler-Mascheroni_sabiti&veaction=edit&section=5" title="Değiştirilen bölüm: Zeta fonksiyonu ile ilişkisi" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Euler-Mascheroni_sabiti&action=edit&section=5" title="Bölümün kaynak kodunu değiştir: Zeta fonksiyonu ile ilişkisi"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pozitif tam sayı içeren <a href="/wiki/Riemann_zeta_i%C5%9Flevi" title="Riemann zeta işlevi">Riemann zeta fonksiyonu</a>'nun <a href="/w/index.php?title=Series_(mathematics)&action=edit&redlink=1" class="new" title="Series (mathematics) (sayfa mevcut değil)">sonsuz toplamı</a> γ sabitine yakınsar: </p> <dl><dd><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{aligned}\gamma &=\sum _{m=2}^{\infty }(-1)^{m}{\frac {\zeta (m)}{m}}\\&=\ln \left({\frac {4}{\pi }}\right)+\sum _{m=2}^{\infty }(-1)^{m}{\frac {\zeta (m)}{2^{m-1}m}}.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>γ</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ζ</mi> <mo stretchy="false">(</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mrow> <mi>m</mi> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mi>π</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ζ</mi> <mo stretchy="false">(</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mi>m</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\gamma &=\sum _{m=2}^{\infty }(-1)^{m}{\frac {\zeta (m)}{m}}\\&=\ln \left({\frac {4}{\pi }}\right)+\sum _{m=2}^{\infty }(-1)^{m}{\frac {\zeta (m)}{2^{m-1}m}}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7bdc84ada4a51308a849e9da179db31b5f158e5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.505ex; width:33.941ex; height:14.176ex;" alt="{\displaystyle {\begin{aligned}\gamma &=\sum _{m=2}^{\infty }(-1)^{m}{\frac {\zeta (m)}{m}}\\&=\ln \left({\frac {4}{\pi }}\right)+\sum _{m=2}^{\infty }(-1)^{m}{\frac {\zeta (m)}{2^{m-1}m}}.\end{aligned}}}"></span></dd></dl> <p>zeta fonksiyonu içeren diğer serilerle ilişkisi: </p> <dl><dd><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{aligned}\gamma &={\frac {3}{2}}-\ln 2-\sum _{m=2}^{\infty }(-1)^{m}\,{\frac {m-1}{m}}[\zeta (m)-1]\\&=\lim _{n\to \infty }\left[{\frac {2\,n-1}{2\,n}}-\ln \,n+\sum _{k=2}^{n}\left({\frac {1}{k}}-{\frac {\zeta (1-k)}{n^{k}}}\right)\right]\\&=\lim _{n\to \infty }\left[{\frac {2^{n}}{e^{2^{n}}}}\sum _{m=0}^{\infty }{\frac {2^{m\,n}}{(m+1)!}}\sum _{t=0}^{m}{\frac {1}{t+1}}-n\,\ln 2+O\left({\frac {1}{2^{n}\,e^{2^{n}}}}\right)\right].\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>γ</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> <mo>−</mo> <mi>ln</mi> <mo>⁡</mo> <mn>2</mn> <mo>−</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>m</mi> <mo>−</mo> <mn>1</mn> </mrow> <mi>m</mi> </mfrac> </mrow> <mo stretchy="false">[</mo> <mi>ζ</mi> <mo stretchy="false">(</mo> <mi>m</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow> <mo>[</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mspace width="thinmathspace" /> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <mn>2</mn> <mspace width="thinmathspace" /> <mi>n</mi> </mrow> </mfrac> </mrow> <mo>−</mo> <mi>ln</mi> <mspace width="thinmathspace" /> <mi>n</mi> <mo>+</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>k</mi> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ζ</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>k</mi> <mo stretchy="false">)</mo> </mrow> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow> <mo>[</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mrow> </msup> </mfrac> </mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mspace width="thinmathspace" /> <mi>n</mi> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>−</mo> <mi>n</mi> <mspace width="thinmathspace" /> <mi>ln</mi> <mo>⁡</mo> <mn>2</mn> <mo>+</mo> <mi>O</mi> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mspace width="thinmathspace" /> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\gamma &={\frac {3}{2}}-\ln 2-\sum _{m=2}^{\infty }(-1)^{m}\,{\frac {m-1}{m}}[\zeta (m)-1]\\&=\lim _{n\to \infty }\left[{\frac {2\,n-1}{2\,n}}-\ln \,n+\sum _{k=2}^{n}\left({\frac {1}{k}}-{\frac {\zeta (1-k)}{n^{k}}}\right)\right]\\&=\lim _{n\to \infty }\left[{\frac {2^{n}}{e^{2^{n}}}}\sum _{m=0}^{\infty }{\frac {2^{m\,n}}{(m+1)!}}\sum _{t=0}^{m}{\frac {1}{t+1}}-n\,\ln 2+O\left({\frac {1}{2^{n}\,e^{2^{n}}}}\right)\right].\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c4a5413d5b0a6c08764cd0e62fd121a9012015b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -10.505ex; width:64.543ex; height:22.176ex;" alt="{\displaystyle {\begin{aligned}\gamma &={\frac {3}{2}}-\ln 2-\sum _{m=2}^{\infty }(-1)^{m}\,{\frac {m-1}{m}}[\zeta (m)-1]\\&=\lim _{n\to \infty }\left[{\frac {2\,n-1}{2\,n}}-\ln \,n+\sum _{k=2}^{n}\left({\frac {1}{k}}-{\frac {\zeta (1-k)}{n^{k}}}\right)\right]\\&=\lim _{n\to \infty }\left[{\frac {2^{n}}{e^{2^{n}}}}\sum _{m=0}^{\infty }{\frac {2^{m\,n}}{(m+1)!}}\sum _{t=0}^{m}{\frac {1}{t+1}}-n\,\ln 2+O\left({\frac {1}{2^{n}\,e^{2^{n}}}}\right)\right].\end{aligned}}}"></span></dd></dl> <p>Son denklemde n sayısı nedeniyle hata teriminin hızla azalması hesaplama için uygundur. </p><p>Diğer ilginç limit eşitliği Euler–Mascheroni sabitinin antisimetrik limitidir. (Sondow, 1998) </p> <dl><dd><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 \gamma =\lim _{s\to 1^{+}}\sum _{n=1}^{\infty }\left({\frac {1}{n^{s}}}-{\frac {1}{s^{n}}}\right)=\lim _{s\to 1}\left(\zeta (s)-{\frac {1}{s-1}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo stretchy="false">→</mo> <msup> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> </munder> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msup> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo stretchy="false">→</mo> <mn>1</mn> </mrow> </munder> <mrow> <mo>(</mo> <mrow> <mi>ζ</mi> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>s</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma =\lim _{s\to 1^{+}}\sum _{n=1}^{\infty }\left({\frac {1}{n^{s}}}-{\frac {1}{s^{n}}}\right)=\lim _{s\to 1}\left(\zeta (s)-{\frac {1}{s-1}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3a6acf56ca8eddd7fd6031cd363de13dc989ec8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:48.477ex; height:6.843ex;" alt="{\displaystyle \gamma =\lim _{s\to 1^{+}}\sum _{n=1}^{\infty }\left({\frac {1}{n^{s}}}-{\frac {1}{s^{n}}}\right)=\lim _{s\to 1}\left(\zeta (s)-{\frac {1}{s-1}}\right)}"></span></dd></dl> <p>ve </p> <dl><dd><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{aligned}\gamma =\lim _{n\to \infty }{\frac {1}{n}}\,\sum _{k=1}^{n}\left(\left\lceil {\frac {n}{k}}\right\rceil -{\frac {n}{k}}\right).\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>γ</mi> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mrow> <mo>(</mo> <mrow> <mrow> <mo>⌈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>n</mi> <mi>k</mi> </mfrac> </mrow> <mo>⌉</mo> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>n</mi> <mi>k</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\gamma =\lim _{n\to \infty }{\frac {1}{n}}\,\sum _{k=1}^{n}\left(\left\lceil {\frac {n}{k}}\right\rceil -{\frac {n}{k}}\right).\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/984761e6ed8782444be6c003cb5b261464653795" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:30.085ex; height:6.843ex;" alt="{\displaystyle {\begin{aligned}\gamma =\lim _{n\to \infty }{\frac {1}{n}}\,\sum _{k=1}^{n}\left(\left\lceil {\frac {n}{k}}\right\rceil -{\frac {n}{k}}\right).\end{aligned}}}"></span></dd></dl> <p><a href="/w/index.php?title=Rasyonel_zeta_serisi&action=edit&redlink=1" class="new" title="Rasyonel zeta serisi (sayfa mevcut değil)">rasyonel zeta serisi</a> ifadesi ile de yakında ilişkilidir. </p> <dl><dd><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 \gamma =\sum _{k=1}^{n}{\frac {1}{k}}-\ln n-\sum _{m=2}^{\infty }{\frac {\zeta (m,n+1)}{m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>k</mi> </mfrac> </mrow> <mo>−</mo> <mi>ln</mi> <mo>⁡</mo> <mi>n</mi> <mo>−</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ζ</mi> <mo stretchy="false">(</mo> <mi>m</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mi>m</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma =\sum _{k=1}^{n}{\frac {1}{k}}-\ln n-\sum _{m=2}^{\infty }{\frac {\zeta (m,n+1)}{m}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55eb3465f12d5235989cd2845ac186400cb8b719" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:35.695ex; height:6.843ex;" alt="{\displaystyle \gamma =\sum _{k=1}^{n}{\frac {1}{k}}-\ln n-\sum _{m=2}^{\infty }{\frac {\zeta (m,n+1)}{m}}}"></span></dd></dl> <p>Burada ζ(<i>s</i>,<i>k</i>) <a href="/wiki/Hurwitz_zeta_fonksiyonu" title="Hurwitz zeta fonksiyonu">Hurwitz zeta fonksiyonu</a>'dur. Bu denklem <a href="/w/index.php?title=Harmonik_say%C4%B1lar&action=edit&redlink=1" class="new" title="Harmonik sayılar (sayfa mevcut değil)">harmonik sayılar</a>'ın toplamını içermektedir., <i>H</i><sub><i>n</i></sub>. Hurwitz zeta fonksiyonu'nun açılımındaki bazı terimler: </p> <dl><dd><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 H_{n}=\ln n+\gamma +{\frac {1}{2n}}-{\frac {1}{12n^{2}}}+{\frac {1}{120n^{4}}}-\varepsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mi>n</mi> <mo>+</mo> <mi>γ</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>12</mn> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>120</mn> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>−</mo> <mi>ε</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{n}=\ln n+\gamma +{\frac {1}{2n}}-{\frac {1}{12n^{2}}}+{\frac {1}{120n^{4}}}-\varepsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/190051a902445567cbec9ad845f34cd9c78cf9e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:42.293ex; height:5.509ex;" alt="{\displaystyle H_{n}=\ln n+\gamma +{\frac {1}{2n}}-{\frac {1}{12n^{2}}}+{\frac {1}{120n^{4}}}-\varepsilon }"></span>, burada <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 0<\varepsilon <{\frac {1}{252n^{6}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo><</mo> <mi>ε</mi> <mo><</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>252</mn> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0<\varepsilon <{\frac {1}{252n^{6}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a253cb043ead35fb9963e3d76766250543eba22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.862ex; height:5.509ex;" alt="{\displaystyle 0<\varepsilon <{\frac {1}{252n^{6}}}.}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Notlar">Notlar</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Euler-Mascheroni_sabiti&veaction=edit&section=6" title="Değiştirilen bölüm: Notlar" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Euler-Mascheroni_sabiti&action=edit&section=6" title="Bölümün kaynak kodunu değiştir: Notlar"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r32805677">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-count:2}.mw-parser-output .reflist-columns-3{column-count:3}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><strong><a href="#cite_ref-1">^</a></strong> <span class="reference-text">Krämer 2005</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Kaynakça"><span id="Kaynak.C3.A7a"></span>Kaynakça</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Euler-Mascheroni_sabiti&veaction=edit&section=7" title="Değiştirilen bölüm: Kaynakça" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Euler-Mascheroni_sabiti&action=edit&section=7" title="Bölümün kaynak kodunu değiştir: Kaynakça"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="kaynak dergi">Borwein, Jonathan M., David M. Bradley, Richard E. Crandall (2000). "<a rel="nofollow" class="external text" href="http://www.maths.ex.ac.uk/~mwatkins/zeta/borwein1.pdf">Computational Strategies for the Riemann Zeta Function</a>". <i>Journal of Computational and Applied Mathematics</i>. Cilt 121. s. 11.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=%5Bhttp%3A%2F%2Fwww.maths.ex.ac.uk%2F~mwatkins%2Fzeta%2Fborwein1.pdf+Computational+Strategies+for+the+Riemann+Zeta+Function%5D&rft.pages=11&rft.date=2000&rft.au=Borwein%2C+Jonathan+M.%2C+David+M.+Bradley%2C+Richard+E.+Crandall&rfr_id=info%3Asid%2Ftr.wikipedia.org%3AEuler-Mascheroni+sabiti" class="Z3988"><span style="display:none;"> </span></span> <span style="font-size:100%" class="error citation-comment"><code style="color:inherit; border:inherit; padding:inherit;">|başlık=</code> dış bağlantı (<a href="/wiki/Yard%C4%B1m:KB1_hatalar%C4%B1#param_has_ext_link" title="Yardım:KB1 hataları">yardım</a>)</span><span class="citation-comment" style="display:none; color:#33aa33; margin-left:0.3em">KB1 bakım: Birden fazla ad: yazar listesi (<a href="/wiki/Kategori:KB1_bak%C4%B1m:_Birden_fazla_ad:_yazar_listesi" title="Kategori:KB1 bakım: Birden fazla ad: yazar listesi">link</a>) </span> Derives γ as sums over Riemann zeta functions.</li> <li>Gourdon, Xavier, and Sebah, P. (2002) "<a rel="nofollow" class="external text" href="http://numbers.computation.free.fr/Constants/Gamma/gammaFormulas.html">Collection of formulas for Euler's constant, γ.</a> 12 Aralık 2009 tarihinde <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> sitesinde <a rel="nofollow" class="external text" href="https://web.archive.org/web/20091212002936/http://numbers.computation.free.fr/Constants/Gamma/gammaFormulas.html">arşivlendi</a>."</li> <li>----- (2004) "<a rel="nofollow" class="external text" href="http://numbers.computation.free.fr/Constants/Gamma/gamma.html">The Euler constant: γ.</a> 28 Nisan 2009 tarihinde <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> sitesinde <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090428001402/http://numbers.computation.free.fr/Constants/Gamma/gamma.html">arşivlendi</a>."</li> <li><a href="/wiki/Donald_Knuth" title="Donald Knuth">Donald Knuth</a> (1997) <i><a href="/wiki/The_Art_of_Computer_Programming" title="The Art of Computer Programming">The Art of Computer Programming</a>, Vol. 1</i>, 3rd ed. Addison-Wesley. <a href="/wiki/%C3%96zel:KitapKaynaklar%C4%B1/0201896834" class="internal mw-magiclink-isbn">ISBN 0-201-89683-4</a></li> <li>Krämer, Stefan (2005) <i>Die Eulersche Konstante γ und verwandte Zahlen</i>. Diplomarbeit, Universität Göttingen.</li> <li>Sondow, Jonathan (1998) "<a rel="nofollow" class="external text" href="https://web.archive.org/web/20060808201434/http://home.earthlink.net/~jsondow/id8.html">An antisymmetric formula for Euler's constant,</a>" <i><a href="/w/index.php?title=Mathematics_Magazine&action=edit&redlink=1" class="new" title="Mathematics Magazine (sayfa mevcut değil)">Mathematics Magazine</a> 71</i>: 219-220.</li> <li>------ (2002) "<a rel="nofollow" class="external text" href="http://arXiv.org/abs/math.NT/0211075">A hypergeometric approach, via linear forms involving logarithms, to irrationality criteria for Euler's constant.</a>" With an Appendix by <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130523085959/http://wain.mi.ras.ru/zlobin/">Sergey Zlobin</a>, Mathematica Slovaca 59<i>: 307-314.</i></li> <li>------ (2003) "<a rel="nofollow" class="external text" href="http://arXiv.org/abs/math.CA/0306008">An infinite product for e<sup>γ</sup> via hypergeometric formulas for Euler's constant, γ.</a>"</li> <li>------ (2003a) "<a rel="nofollow" class="external text" href="http://arXiv.org/abs/math.NT/0209070">Criteria for irrationality of Euler's constant,</a>" <i><a href="/w/index.php?title=Proceedings_of_the_American_Mathematical_Society&action=edit&redlink=1" class="new" title="Proceedings of the American Mathematical Society (sayfa mevcut değil)">Proceedings of the American Mathematical Society</a> 131</i>: 3335-3344.</li> <li>------ (2005) "<a rel="nofollow" class="external text" href="http://arXiv.org/abs/math.CA/0211148">Double integrals for Euler's constant and ln 4/π and an analog of Hadjicostas's formula,</a>" <i><a href="/w/index.php?title=American_Mathematical_Monthly&action=edit&redlink=1" class="new" title="American Mathematical Monthly (sayfa mevcut değil)">American Mathematical Monthly</a> 112</i>: 61-65.</li> <li>------ (2005) <a rel="nofollow" class="external text" href="http://arXiv.org/abs/math.NT/0508042">"New Vacca-type rational series for Euler's constant and its 'alternating' analog ln 4/π.</a>"</li> <li>------ and <a href="/w/index.php?title=Wadim_Zudilin&action=edit&redlink=1" class="new" title="Wadim Zudilin (sayfa mevcut değil)">Wadim Zudilin</a> (2006), <a rel="nofollow" class="external text" href="http://arXiv.org/abs/math.NT/0304021">"Euler's constant, q-logarithms, and formulas of Ramanujan and Gosper,"</a> Ramanujan Journal 12<i>: 225-244.</i></li> <li>G. Vacca (1926), "Nuova serie per la costante di Eulero, <i>C</i> = 0,577…". <i>Rendiconti, Accademia Nazionale dei Lincei, Roma, Classe di Scienze Fisiche, Matematiche e Naturali</i> (6) 3, 19–20.</li> <li><a href="/w/index.php?title=James_Whitbread_Lee_Glaisher&action=edit&redlink=1" class="new" title="James Whitbread Lee Glaisher (sayfa mevcut değil)">James Whitbread Lee Glaisher</a> (1872), "On the history of Euler's constant". Messenger of Mathematics. New Series, vol.1, p. 25-30, JFM 03.0130.01</li> <li>Carl Anton Bretschneider (1837). "Theoriae logarithmi integralis lineamenta nova". Crelle Journal, vol.17, p. 257-285 (submitted 1835)</li> <li><a href="/w/index.php?title=Lorenzo_Mascheroni&action=edit&redlink=1" class="new" title="Lorenzo Mascheroni (sayfa mevcut değil)">Lorenzo Mascheroni</a> (1790). "Adnotationes ad calculum integralem Euleri, in quibus nonnulla problemata ab Eulero proposita resolvuntur". Galeati, Ticini.</li> <li><a href="/w/index.php?title=Lorenzo_Mascheroni&action=edit&redlink=1" class="new" title="Lorenzo Mascheroni (sayfa mevcut değil)">Lorenzo Mascheroni</a> (1792). "Adnotationes ad calculum integralem Euleri. In quibus nonnullae formulae ab Eulero propositae evolvuntur". Galeati, Ticini. Both online at: <a rel="nofollow" class="external free" href="http://books.google.de/books?id=XkgDAAAAQAAJ">http://books.google.de/books?id=XkgDAAAAQAAJ</a> 24 Ekim 2012 tarihinde <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> sitesinde <a rel="nofollow" class="external text" href="https://web.archive.org/web/20121024193226/http://books.google.de/books?id=XkgDAAAAQAAJ">arşivlendi</a>.</li> <li><cite class="kaynak kitap">Havil, Julian (2003). <a rel="nofollow" class="external text" href="https://archive.org/details/gammaexploringeu0000havi"><i>Gamma: Exploring Euler's Constant</i></a>. Princeton University Press. <a href="/wiki/Uluslararas%C4%B1_Standart_Kitap_Numaras%C4%B1" title="Uluslararası Standart Kitap Numarası">ISBN</a> <a href="/wiki/%C3%96zel:KitapKaynaklar%C4%B1/0-691-09983-9" title="Özel:KitapKaynakları/0-691-09983-9">0-691-09983-9</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gamma%3A+Exploring+Euler%27s+Constant&rft.pub=Princeton+University+Press&rft.date=2003&rft.isbn=0-691-09983-9&rft.aulast=Havil&rft.aufirst=Julian&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fgammaexploringeu0000havi&rfr_id=info%3Asid%2Ftr.wikipedia.org%3AEuler-Mascheroni+sabiti" class="Z3988"><span style="display:none;"> </span></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Dış_bağlantılar"><span id="D.C4.B1.C5.9F_ba.C4.9Flant.C4.B1lar"></span>Dış bağlantılar</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Euler-Mascheroni_sabiti&veaction=edit&section=8" title="Değiştirilen bölüm: Dış bağlantılar" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Euler-Mascheroni_sabiti&action=edit&section=8" title="Bölümün kaynak kodunu değiştir: Dış bağlantılar"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="kaynak web">Krämer, Stefan. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131017040641/http://www.math.uni-goettingen.de/skraemer/gamma.html">"Euler's Constant γ=0.577... Its Mathematics and History"</a>. 17 Ekim 2017 tarihinde <a rel="nofollow" class="external text" href="http://www.math.uni-goettingen.de/skraemer/gamma.html">kaynağından</a> arşivlendi.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Euler%27s+Constant+%CE%B3%3D0.577...+Its+Mathematics+and+History&rft.au=Kr%C3%A4mer%2C+Stefan&rft_id=http%3A%2F%2Fwww.math.uni-goettingen.de%2Fskraemer%2Fgamma.html&rfr_id=info%3Asid%2Ftr.wikipedia.org%3AEuler-Mascheroni+sabiti" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="kaynak web"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20071210200421/http://home.earthlink.net/~jsondow/">"Jonathan Sondow"</a>. 10 Aralık 2007 tarihinde <a rel="nofollow" class="external text" href="https://home.earthlink.net/~jsondow/">kaynağından</a> arşivlendi.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Jonathan+Sondow&rft_id=http%3A%2F%2Fhome.earthlink.net%2F~jsondow%2F&rfr_id=info%3Asid%2Ftr.wikipedia.org%3AEuler-Mascheroni+sabiti" class="Z3988"><span style="display:none;"> </span></span></li></ul> <div role="navigation" class="navbox" aria-labelledby="Leonhard_Euler" style="padding:3px"><table class="nowraplinks collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><style data-mw-deduplicate="TemplateStyles:r25548259">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ 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href="/w/index.php?title=Euler-Tricomi_denklemi&action=edit&redlink=1" class="new" title="Euler-Tricomi denklemi (sayfa mevcut değil)">Euler-Tricomi denklemi</a></li> <li><a href="/w/index.php?title=Euler_s%C3%BCrekli_kesirler_form%C3%BCl%C3%BC&action=edit&redlink=1" class="new" title="Euler sürekli kesirler formülü (sayfa mevcut değil)">Euler sürekli kesirler formülü</a></li> <li><a href="/w/index.php?title=Euler_kritik_y%C3%BCk%C3%BC&action=edit&redlink=1" class="new" title="Euler kritik yükü (sayfa mevcut değil)">Euler kritik yükü</a></li> <li><a href="/wiki/Euler_form%C3%BCl%C3%BC" title="Euler formülü">Euler formülü</a></li> <li><a href="/w/index.php?title=Euler_d%C3%B6rt-kare_%C3%B6zde%C5%9Fli%C4%9Fi&action=edit&redlink=1" class="new" title="Euler dört-kare özdeşliği (sayfa mevcut değil)">Euler dört-kare özdeşliği</a></li> <li><a href="/wiki/Euler_%C3%B6zde%C5%9Fli%C4%9Fi" title="Euler özdeşliği">Euler özdeşliği</a></li> <li><a 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title="Euler fonksiyonu (sayfa mevcut değil)">Euler fonksiyonu</a></li> <li><a href="/wiki/Euler_y%C3%B6ntemi" title="Euler yöntemi">Euler yöntemi</a></li> <li><a href="/wiki/Euler_say%C4%B1lar%C4%B1" title="Euler sayıları">Euler sayıları</a></li> <li><a href="/wiki/Euler_say%C4%B1s%C4%B1_(fizik)" title="Euler sayısı (fizik)">Euler sayısı (fizik)</a></li> <li><a href="/w/index.php?title=Euler-Bernoulli_kiri%C5%9F_teorisi&action=edit&redlink=1" class="new" title="Euler-Bernoulli kiriş teorisi (sayfa mevcut değil)">Euler-Bernoulli kiriş teorisi</a></li> <li><a href="/wiki/Euler_teoremi_(geometri)" title="Euler teoremi (geometri)">Euler teoremi (geometri)</a></li> <li><a href="/wiki/Euler_spirali" title="Euler spirali">Euler spirali</a></li> <li><a href="/wiki/Euler-Fuss_denklemi" title="Euler-Fuss denklemi">Euler-Fuss denklemi</a></li> <li><a href="/wiki/Euler_d%C3%B6rtgen_teoremi" title="Euler dörtgen teoremi">Euler dörtgen teoremi</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Diğer</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/w/index.php?title=Leonhard_Euler%27in_ad%C4%B1n%C4%B1_ta%C5%9F%C4%B1yan_%C5%9Feylerin_listesi&action=edit&redlink=1" class="new" title="Leonhard Euler'in adını taşıyan şeylerin listesi (sayfa mevcut değil)">Aynı adı taşıyan</a></li> <li><a href="/w/index.php?title=Euler_Committee&action=edit&redlink=1" class="new" title="Euler Committee (sayfa mevcut değil)">Euler Committee</a></li> <li><a href="/w/index.php?title=Johann_Euler&action=edit&redlink=1" class="new" title="Johann Euler (sayfa mevcut değil)">Johann Euler</a></li> <li><a href="/wiki/Johann_Bernoulli" title="Johann Bernoulli">Johann Bernoulli</a> (<a href="/wiki/Bernoulli_ailesi" title="Bernoulli ailesi">Bernoulli ailesi</a>)</li> <li><a href="/w/index.php?title=Georg_Gsell&action=edit&redlink=1" 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