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mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-14 ns-subject mw-editable page-Category_Bernoulli_numbers rootpage-Category_Bernoulli_numbers skin-vector action-view"><div id="mw-page-base" class="noprint"></div> <div id="mw-head-base" class="noprint"></div> <div id="content" class="mw-body" role="main"> <a id="top"></a> <div id="siteNotice"><!-- CentralNotice --></div> <div class="mw-indicators"> <div id="mw-indicator-mw-helplink" class="mw-indicator"><a href="/wiki/Commons:Categories" target="_blank" class="mw-helplink"><span class="mw-helplink-icon"></span>Help</a></div> </div> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-namespace">Category</span><span class="mw-page-title-separator">:</span><span class="mw-page-title-main">Bernoulli numbers</span></h1> <div id="bodyContent" class="vector-body"> <div id="siteSub" class="noprint">From Wikimedia Commons, the free media repository</div> <div id="contentSub"><div id="mw-content-subtitle"><div class="cdx-message cdx-message--block cdx-message--warning mw-revision"><span class="cdx-message__icon"></span><div class="cdx-message__content"><div id="mw-revision-info">Revision as of 10:37, 25 November 2019 by <a href="/wiki/User:Pi_bot" class="mw-userlink" title="User:Pi bot" data-mw-revid="377796888"><bdi>Pi bot</bdi></a> <span class="mw-usertoollinks">(<a href="/wiki/User_talk:Pi_bot" class="mw-redirect mw-usertoollinks-talk" title="User talk:Pi bot">talk</a> | <a href="/wiki/Special:Contributions/Pi_bot" class="mw-usertoollinks-contribs" title="Special:Contributions/Pi bot">contribs</a>)</span> <span class="comment">(Adding {{Wikidata Infobox}}, current Wikidata ID is Q694114)</span></div><div id="mw-revision-nav">(<a href="/w/index.php?title=Category:Bernoulli_numbers&diff=prev&oldid=377796888" title="Category:Bernoulli numbers">diff</a>) <a href="/w/index.php?title=Category:Bernoulli_numbers&direction=prev&oldid=377796888" title="Category:Bernoulli numbers">← Older 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#wdinfoboxcaption{margin-right:0}.mw-parser-output #wdinfobox th,.mw-parser-output #wdinfo_taxon th{vertical-align:top;word-wrap:break-word;hyphens:auto}.mw-parser-output #wdinfobox td,.mw-parser-output #wdinfo_taxon td{word-wrap:break-word;hyphens:auto}.mw-parser-output #wdinfobox li:not(:last-child){margin-bottom:3px}.mw-parser-output #wdinfo_taxon{font-size:95%;table-layout:fixed;padding:0}.mw-parser-output .taxontree-lcell,.mw-parser-output .wikidatainfobox-lcell{background:#CFE3FF;padding-left:.4em;padding-right:.4em;font-weight:bold}.mw-parser-output .taxontree-rcell,.mw-parser-output .wikidatainfobox-rcell{word-wrap:break-word;hyphens:auto}.mw-parser-output #wdinfobox[dir="ltr"] .taxontree-lcell,.mw-parser-output #wdinfobox[dir="ltr"] .wikidatainfobox-lcell{text-align:right;word-wrap:break-word;hyphens:auto}.mw-parser-output #wdinfobox[dir="rtl"] .taxontree-lcell,.mw-parser-output #wdinfobox[dir="rtl"] .wikidatainfobox-lcell{text-align:left;word-wrap:break-word;hyphens:auto}.mw-parser-output .taxontree-fullcell{text-align:center}.mw-parser-output .taxontree-hdrcell{text-align:center;background:#CFE3FF;padding-left:.4em;padding-right:.4em;font-weight:bold}.mw-parser-output .taxontree-row{}@media screen and (max-width:600px){.mw-parser-output .wdinfo_nomobile{display:none;visibility:hidden;height:0}}.mw-parser-output .wdinfobox_horizontal{clear:both!important;display:block;box-sizing:border-box!important;width:100%!important;column-width:24em}.mw-parser-output .wdinfobox_hide{display:none}.mw-parser-output #wdcreator{display:none}.mw-parser-output .wdcreator_show{display:block!important}.mw-parser-output #wdinfo_taxon ul{list-style:none;list-style-position:inside}.mw-parser-output #wdinfobox[dir="ltr"] #wdinfo_taxon ul{padding-left:0;margin-left:0}.mw-parser-output #wdinfobox[dir="rtl"] #wdinfo_taxon ul{padding-right:0;margin-right:0}.mw-parser-output .wikidatainfoboxVN ul li{list-style:none;padding:0;margin:0}.mw-parser-output .wikidatainfoboxVN ul{margin-left:0}.mw-parser-output .wikidatainfoboxVN{padding:0;margin:0}</style><div style="display:none"><nowiki>número de Bernoulli; 白努利數; Bernoulli-számok; Bernouilliren zenbaki; число Бернулли; Bernoulli-Zahl; عدد برنولی; 伯努利数; număr Bernoulli; ベルヌーイ数; Bernoullital; מספרי ברנולי; 伯努利數; बर्नूली संख्या; Bernoulli sonlari; Бернулли сандары; nombroj de Bernoulli; Bernoulliho číslo; numero di Bernoulli; nombre de Bernoulli; 伯努利數; 伯努利数; Бернулијеви бројеви; Bernulijevi brojevi; برنولی عدد; número de Bernoulli; số Bernoulli; بەرنۋللىي ساندارى; Bernulli skaitlis; Bernoullin luku; Бернулијеви бројеви; Bernoullijevo število; 베르누이 수; Bernoulligetal; Бернулли сандары; จำนวนแบร์นูลลี; liczby Bernoulliego; Bernoulli-tall; Bernulli ədədləri; Nombres de Bernoulli; Bernoulli sayısı; Числа на Бернули; Bernwllï sandarı; Bernoulli number; عدد برنولي; Αριθμός Bernoulli; число Бернуллі; numeri che costituiscono una successione di numeri razionali; suite de nombres rationnels; nieskończony ciąg liczb niewymiernych; סדרת מספרים בעלת תכונות מתמטיות חשובות; 實數數列; Folge rationaler Zahlen; rationaalilukujono; rational number sequence 𝐵ₖ such that (𝑚+1)∑𝑛ᵐ=(ᵐ⁺¹₀)𝐵₀𝑛ᵐ⁺¹−(ᵐ⁺¹₁)𝐵₁𝑛ᵐ+(ᵐ⁺¹₂)𝐵₂𝑛ᵐ¯¹−(ᵐ⁺¹₃)𝐵₃𝑛ᵐ¯²+⋯; vico de racionaloj 𝐵ₖ tiaj ke (𝑚+1)∑𝑛ᵐ=(ᵐ⁺¹₀)𝐵₀𝑛ᵐ⁺¹−(ᵐ⁺¹₁)𝐵₁𝑛ᵐ+(ᵐ⁺¹₂)𝐵₂𝑛ᵐ¯¹−(ᵐ⁺¹₃)𝐵₃𝑛ᵐ¯²+⋯; números de Bernoulli; nombres de Bernoulli; числа Бернулли; Bernoullizahl; Bernoullische Zahlen; Bernoullische Zahl; Bernoullizahlen; Bernoullipolynom; Bernoulli-Zahlen; números de Bernoulli; Bernoulli数; 伯努利數; Bernoulli sayıları; Von Staudt-Clausens sats; Bernoullis tal; Mohammed Altoumaimi; Von Staudt-Clausens formel; Bernoulliska talen; Bernoullitalen; liczby Bernoullego; מספר ברנולי; Bernoulli-getal; Bernoulli getallen; Bernoullijeva števila; числа Бернуллі; numeri di Bernoulli; Bernoullin luvut; Bernoulli numbers; أعداد برنولي; أعداد بيرنولي; Αριθμός Μπερνούλι; Берноулли сонлари; Bernoulli raqamlari; Bernulli sonlari; Bernulli-raqamlari</nowiki></div><table id="wdinfobox" class="fileinfotpl-type-information vevent infobox mw-collapsible mw-content-ltr"><caption class="fn org" id="wdinfoboxcaption"><b>Bernoulli number </b></caption><tbody><tr><td colspan="2" class="wdinfo_nomobile" style="text-align:center"><div>rational number sequence 𝐵ₖ such that (𝑚+1)∑𝑛ᵐ=(ᵐ⁺¹₀)𝐵₀𝑛ᵐ⁺¹−(ᵐ⁺¹₁)𝐵₁𝑛ᵐ+(ᵐ⁺¹₂)𝐵₂𝑛ᵐ¯¹−(ᵐ⁺¹₃)𝐵₃𝑛ᵐ¯²+⋯</div><div class="switcher-container"><div class="center"><span class="wpImageAnnotatorControl wpImageAnnotatorCaptionOff"><span typeof="mw:File"><a href="/wiki/File:Bernoulli_numbers_logarithmic_growth.png" class="mw-file-description"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/08/Bernoulli_numbers_logarithmic_growth.png/230px-Bernoulli_numbers_logarithmic_growth.png" decoding="async" width="230" height="192" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/0/08/Bernoulli_numbers_logarithmic_growth.png/345px-Bernoulli_numbers_logarithmic_growth.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/0/08/Bernoulli_numbers_logarithmic_growth.png/460px-Bernoulli_numbers_logarithmic_growth.png 2x" data-file-width="480" data-file-height="400" /></a></span></span></div></div></td></tr><tr><td colspan="2" style="text-align:center"><b><a class="external text" href="https://commons.wikimedia.org/w/index.php?title=Special%3AUploadWizard&categories=Bernoulli+numbers">Upload media</a></b></td></tr><tr><td colspan="2" style="text-align:center; font-weight:bold"><div><span typeof="mw:File"><span><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/16px-Wikipedia-logo-v2.svg.png" decoding="async" width="16" height="15" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/24px-Wikipedia-logo-v2.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/32px-Wikipedia-logo-v2.svg.png 2x" data-file-width="103" data-file-height="94" /></span></span> <a href="https://en.wikipedia.org/wiki/Bernoulli_number" class="extiw" title="en:Bernoulli number">Wikipedia</a></div></td></tr><tr><th class="wikidatainfobox-lcell">Instance of</th><td><div class="plainlist"><ul><li>sequence of real numbers</li><li><a href="/wiki/Category:Mathematical_concepts" title="Category:Mathematical concepts">mathematical concept</a></li></ul></div></td></tr><tr class="wdinfo_nomobile"><th class="wikidatainfobox-lcell">Subclass of</th><td><div class="plainlist"><ul><li><a href="/wiki/Category:Rational_numbers" title="Category:Rational numbers">rational number</a></li></ul></div></td></tr><tr class="wdinfo_nomobile"><th class="wikidatainfobox-lcell">Named after</th><td><div class="plainlist"><ul><li><a href="/wiki/Category:Jakob_Bernoulli" title="Category:Jakob Bernoulli">Jacob Bernoulli</a></li></ul></div></td></tr><tr class="wdinfo_nomobile"><th class="wikidatainfobox-lcell">Discoverer or inventor</th><td><div class="plainlist"><ul><li><a href="/wiki/Category:Jakob_Bernoulli" title="Category:Jakob Bernoulli">Jacob Bernoulli</a></li><li><a href="/wiki/Category:Seki_Takakazu" title="Category:Seki Takakazu">Takakazu Seki</a></li></ul></div></td></tr><tr class="wdinfo_nomobile"><th class="wikidatainfobox-lcell">Time of discovery or invention</th><td><div class="plainlist"><ul><li>1710s</li></ul></div></td></tr><tr><td colspan="2"><table style="width:100%" id="wdinfo_ac" class="mw-collapsible"><tbody><tr><th style="background: #cfe3ff">Authority file</th></tr><tr><td style="text-align: center;"><div style="overflow-wrap: break-word; font-size: smaller"><span typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q694114" title="d:Q694114"><img alt="Wikidata" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span> <a href="https://www.wikidata.org/wiki/Q694114" class="extiw" title="d:Q694114">Q694114</a><br /><span class="wdinfo_nomobile"><span typeof="mw:File"><span><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Logo_Gemeinsame_Normdatei_%28GND%29.svg/18px-Logo_Gemeinsame_Normdatei_%28GND%29.svg.png" decoding="async" width="18" height="21" class="mw-file-element" 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href="https://catalogue.bnf.fr/ark:/12148/cb12286125h">12286125h</a></span></span><br />BNCF Thesaurus ID: <span><span><a rel="nofollow" class="external text" href="https://thes.bncf.firenze.sbn.it/termine.php?id=37195">37195</a></span></span><br />NL CR AUT ID: <span><span><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph982960">ph982960</a></span></span><br />J9U ID: <span><span><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007283266005171">987007283266005171</a></span></span></span></div></td></tr><tr class="wdinfo_nomobile"><td colspan="2" style="text-align: center"><small><div class="hlist hlist-separated"><ul><li><span style="white-space:nowrap"><a class="external text" href="https://reasonator.toolforge.org/?q=Q694114">Reasonator</a></span></li><li><span style="white-space:nowrap"><a href="https://iw.toolforge.org/scholia/Q694114" class="extiw" title="toolforge:scholia/Q694114">Scholia</a></span></li><li><span style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://wikidocumentaries-demo.wmcloud.org/Q694114">Wikidocumentaries</a></span></li><li><span style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://petscan.wmflabs.org/?language=commons&categories=Bernoulli_numbers&project=wikimedia&ns%5B6%5D=1">PetScan</a></span></li><li><span style="white-space:nowrap"><a class="external text" href="https://glamtools.toolforge.org/glamorgan.html?&category=Bernoulli_numbers&depth=1&month=last">statistics</a></span></li><li><span style="white-space:nowrap"><a class="external text" href="https://wikimap.toolforge.org/?cat=Bernoulli_numbers&subcats=true&subcatdepth=1&cluster=true">WikiMap</a></span></li><li><span style="white-space:nowrap"><a class="external text" href="https://locator-tool.toolforge.org/#/geolocate?category=Bernoulli_numbers">Locator tool</a></span></li><li><span style="white-space:nowrap"><a class="external text" href="https://kmlexport.toolforge.org/?project=commons&article=Category%3ABernoulli+numbers">KML file</a></span></li><li><a href="/wiki/Special:Search/haswbstatement:P180%3DQ694114" title="Special:Search/haswbstatement:P180=Q694114">Search depicted</a></li></ul></div></small></td></tr></tbody></table></td></tr><tr class="wdinfo_nomobile"><td lang="en" colspan="2" style="text-align:right"><span typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q694114" title="Edit infobox data on Wikidata"><img alt="Edit infobox data on Wikidata" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/23px-Blue_pencil.svg.png 1.5x, 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class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Bernulli_%C9%99d%C9%99dl%C9%99ri" title="Bernulli ədədləri – Azerbaijani" lang="az" hreflang="az" data-title="Bernulli ədədləri" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%B0_%D0%BD%D0%B0_%D0%91%D0%B5%D1%80%D0%BD%D1%83%D0%BB%D0%B8" title="Числа на Бернули – Bulgarian" lang="bg" hreflang="bg" data-title="Числа на Бернули" data-language-autonym="Български" data-language-local-name="Bulgarian" 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/Nombres_de_Bernoulli" title="Nombres de Bernoulli – Catalan" lang="ca" hreflang="ca" data-title="Nombres de Bernoulli" data-language-autonym="Català" data-language-local-name="Catalan" 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/Bernoulliho_%C4%8D%C3%ADslo" title="Bernoulliho číslo – Czech" lang="cs" hreflang="cs" data-title="Bernoulliho číslo" data-language-autonym="Čeština" data-language-local-name="Czech" 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/Bernoulli-Zahl" title="Bernoulli-Zahl – German" lang="de" hreflang="de" data-title="Bernoulli-Zahl" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CF%81%CE%B9%CE%B8%CE%BC%CF%8C%CF%82_%CE%9C%CF%80%CE%B5%CF%81%CE%BD%CE%BF%CF%8D%CE%BB%CE%B9" title="Αριθμός Μπερνούλι – Greek" lang="el" hreflang="el" data-title="Αριθμός Μπερνούλι" data-language-autonym="Ελληνικά" data-language-local-name="Greek" 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/Bernoulli_number" title="Bernoulli number – English" lang="en" hreflang="en" data-title="Bernoulli number" data-language-autonym="English" data-language-local-name="English" 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/N%C3%BAmero_de_Bernoulli" title="Número de Bernoulli – Spanish" lang="es" hreflang="es" data-title="Número de Bernoulli" data-language-autonym="Español" data-language-local-name="Spanish" 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/Bernoulliren_zenbaki" title="Bernoulliren zenbaki – Basque" lang="eu" hreflang="eu" data-title="Bernoulliren zenbaki" data-language-autonym="Euskara" data-language-local-name="Basque" 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%B9%D8%AF%D8%AF_%D8%A8%D8%B1%D9%86%D9%88%D9%84%DB%8C" title="عدد برنولی – Persian" lang="fa" hreflang="fa" data-title="عدد برنولی" data-language-autonym="فارسی" data-language-local-name="Persian" 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/Bernoullin_luku" title="Bernoullin luku – Finnish" lang="fi" hreflang="fi" data-title="Bernoullin luku" data-language-autonym="Suomi" data-language-local-name="Finnish" 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/Nombre_de_Bernoulli" title="Nombre de Bernoulli – French" lang="fr" hreflang="fr" data-title="Nombre de Bernoulli" data-language-autonym="Français" data-language-local-name="French" 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%9E%D7%A1%D7%A4%D7%A8%D7%99_%D7%91%D7%A8%D7%A0%D7%95%D7%9C%D7%99" title="מספרי ברנולי – Hebrew" lang="he" hreflang="he" data-title="מספרי ברנולי" data-language-autonym="עברית" data-language-local-name="Hebrew" 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%AC%E0%A4%B0%E0%A5%8D%E0%A4%A8%E0%A5%82%E0%A4%B2%E0%A5%80_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="बर्नूली संख्या – Hindi" lang="hi" hreflang="hi" data-title="बर्नूली संख्या" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Bernoulli-sz%C3%A1mok" title="Bernoulli-számok – Hungarian" lang="hu" hreflang="hu" data-title="Bernoulli-számok" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Numeri_di_Bernoulli" title="Numeri di Bernoulli – Italian" lang="it" hreflang="it" data-title="Numeri di Bernoulli" data-language-autonym="Italiano" data-language-local-name="Italian" 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/%E3%83%99%E3%83%AB%E3%83%8C%E3%83%BC%E3%82%A4%E6%95%B0" title="ベルヌーイ数 – Japanese" lang="ja" hreflang="ja" data-title="ベルヌーイ数" data-language-autonym="日本語" data-language-local-name="Japanese" 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%91%D0%B5%D1%80%D0%BD%D1%83%D0%BB%D0%BB%D0%B8_%D1%81%D0%B0%D0%BD%D0%B4%D0%B0%D1%80%D1%8B" title="Бернулли сандары – Kazakh" lang="kk" hreflang="kk" data-title="Бернулли сандары" data-language-autonym="Қазақша" data-language-local-name="Kazakh" 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%B2%A0%EB%A5%B4%EB%88%84%EC%9D%B4_%EC%88%98" title="베르누이 수 – Korean" lang="ko" hreflang="ko" data-title="베르누이 수" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Bernulli_skaitlis" title="Bernulli skaitlis – Latvian" lang="lv" hreflang="lv" data-title="Bernulli skaitlis" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Bernoulligetal" title="Bernoulligetal – Dutch" lang="nl" hreflang="nl" data-title="Bernoulligetal" data-language-autonym="Nederlands" data-language-local-name="Dutch" 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/Bernoulli-tall" title="Bernoulli-tall – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Bernoulli-tall" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian 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/Liczby_Bernoulliego" title="Liczby Bernoulliego – Polish" lang="pl" hreflang="pl" data-title="Liczby Bernoulliego" data-language-autonym="Polski" data-language-local-name="Polish" 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/N%C3%BAmeros_de_Bernoulli" title="Números de Bernoulli – Portuguese" lang="pt" hreflang="pt" data-title="Números de Bernoulli" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%B0_%D0%91%D0%B5%D1%80%D0%BD%D1%83%D0%BB%D0%BB%D0%B8" title="Числа Бернулли – Russian" lang="ru" hreflang="ru" data-title="Числа Бернулли" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Bernoulli_number" title="Bernoulli number – Simple English" lang="en-simple" hreflang="en-simple" data-title="Bernoulli number" 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-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Bernoullijevo_%C5%A1tevilo" title="Bernoullijevo število – Slovenian" lang="sl" hreflang="sl" data-title="Bernoullijevo število" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%91%D0%B5%D1%80%D0%BD%D1%83%D0%BB%D0%B8%D1%98%D0%B5%D0%B2%D0%B8_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%B8" title="Бернулијеви бројеви – Serbian" lang="sr" hreflang="sr" data-title="Бернулијеви бројеви" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" 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/Bernoullital" title="Bernoullital – Swedish" lang="sv" hreflang="sv" data-title="Bernoullital" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%81%E0%B8%9A%E0%B8%A3%E0%B9%8C%E0%B8%99%E0%B8%B9%E0%B8%A5%E0%B8%A5%E0%B8%B5" title="จำนวนแบร์นูลลี – Thai" lang="th" hreflang="th" data-title="จำนวนแบร์นูลลี" data-language-autonym="ไทย" data-language-local-name="Thai" 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/Bernoulli_say%C4%B1s%C4%B1" title="Bernoulli sayısı – Turkish" lang="tr" hreflang="tr" data-title="Bernoulli sayısı" data-language-autonym="Türkçe" data-language-local-name="Turkish" 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%A7%D0%B8%D1%81%D0%BB%D0%B0_%D0%91%D0%B5%D1%80%D0%BD%D1%83%D0%BB%D0%BB%D1%96" title="Числа Бернуллі – Ukrainian" lang="uk" hreflang="uk" data-title="Числа Бернуллі" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A8%D8%B1%D9%86%D9%88%D9%84%DB%8C_%D8%B9%D8%AF%D8%AF" title="برنولی عدد – Urdu" lang="ur" hreflang="ur" data-title="برنولی عدد" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Bernoulli_sonlari" title="Bernoulli sonlari – Uzbek" lang="uz" hreflang="uz" data-title="Bernoulli sonlari" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%BC%AF%E5%8A%AA%E5%88%A9%E6%95%B8" title="伯努利數 – Cantonese" lang="yue" hreflang="yue" data-title="伯努利數" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BC%AF%E5%8A%AA%E5%88%A9%E6%95%B0" title="伯努利数 – Chinese" lang="zh" hreflang="zh" data-title="伯努利数" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q694114#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </nav> </div> </div> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 25 November 2019, at 10:37.</li> <li id="footer-info-copyright">Files are available 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