Euler number

<http://www.wikidata.org/entity/Q947015>

integer sequence defined by the Taylor series expansion of the hyperbolic secant function and also appearing in that of the secant function

rdfs:label	"Euler number"@en "Euler number"@en-ca "Euler number"@en-gb "Euler sayıları"@tr "Euler-tall"@nb "Eulergetal"@nl "Eulerjevo število"@sl "Eulersche Zahlen"@de-ch "Eulertal"@sv "bilangan Euler"@id "eulersche Zahlen"@de "nombre d'Euler"@ca "nombre d'Euler"@fr "numero di Eulero"@it "número de Euler"@es "número de Euler"@pt "número de Euler"@pt-br "números de Euler"@gl "Числа Ейлера"@uk "Эйлер хисепĕ"@cv "Эйлеровы числа"@ru "מספרי אוילר"@he "عدد أويلر"@ar "ஆய்லர் எண்"@ta "オイラー数"@ja "尤拉數列"@zh-hant "尤拉數列"@zh-tw "欧拉数"@zh "오일러 수"@ko
skos:altLabel	"Euler numbers"@en "Euler numbers"@uk "bilangan Euler (bilangan bulat)"@id "eulertall"@nb "nombre sécant"@fr "nombres d'Euler"@fr "nombres sécants"@fr "numero de Euler"@es "numeros de Euler"@es "números de Euler"@es "números de Euler"@gl "числа Ейлера ІІ роду"@uk "числа Эйлера"@ru
schema:description	"bilangan bulat"@id "getaltheorie"@nl "integer sequence defined by the Taylor series expansion of the hyperbolic secant function and also appearing in that of the secant function"@en "secuencia de enteros"@es "secuencia enteira definida pola expansión da serie de Taylor da función secante hiperbólica"@gl "suite d'entiers relatifs définie par le développement en série de Taylor de la fonction sécante hyperbolique et apparaissant également dans celui de la fonction sécante"@fr "целые числа, использующиеся при разложении гиперболического секанса в степенной ряд"@ru "متتالية الأعداد الصحيحة"@ar "整數數列"@zh "整數數列"@zh-hant "整數數列"@zh-tw
schema:dateModified	"2026-08-24T17:51:17+00:00"^^xsd:dateTime
schema:version	2535882079
wikibase:identifiers	7
wikibase:sitelinks	22
wikibase:statements	24
p:P1343	wd:statement/Q947015-7F40C891-F6AA-462E-9096-82E8C1574444
p:P138	wd:statement/q947015-AD971325-0AF8-41B5-8986-628E0BEF3BFA
p:P1889	wd:statement/Q947015-215a6a50-435f-3308-435c-e361a1cfae59
	wd:statement/Q947015-82c1e0d3-4258-c29d-267e-4c3b71568926
	wd:statement/Q947015-d72bbb26-49eb-cffd-5970-f68fe8688382
p:P2534	wd:statement/Q947015-29fb5b51-43e3-053b-5e29-3253db92e767
p:P279	wd:statement/Q947015-bc3e6eaa-4254-d687-29f9-4a4daaf9e0dc
p:P2812	wd:statement/Q947015-90C59325-2D2C-4F36-9107-ACD8AE188C18
p:P31	wd:statement/Q947015-8d9098cf-4d3f-3a5e-487a-eddae8d55b40
	wd:statement/Q947015-95568bda-43a4-7f55-44e6-afcf24a27b86
p:P3417	wd:statement/Q947015-51D98F37-9361-4DEE-9B3A-87F55F8EEFB3
	wd:statement/Q947015-A51CDC28-52EE-4255-93A5-38CF89D39374
p:P508	wd:statement/q947015-92B16E47-5242-4AEB-8561-2516A6D11B87
p:P6104	wd:statement/Q947015-C05AD260-D321-414B-B9A1-B4B4710214D0
p:P6366	wd:statement/Q947015-66581530-98F7-4EF8-9743-A1C26F82A46D
p:P646	wd:statement/Q947015-7E9FF245-20F2-43F6-A657-5D3BA4831DFD
p:P7235	wd:statement/Q947015-25a6a35d-4ebe-a1f5-d28d-d6498d4d5126
	wd:statement/Q947015-4a105a54-484f-e08f-9525-d2fd5a2674b3
	wd:statement/Q947015-7bef6fe3-44bd-a568-e0ee-1c8959342ebb
	wd:statement/Q947015-93a93478-441c-7ba6-c4a3-005482926d0f
	wd:statement/Q947015-a2cc8a0c-4116-437a-62a7-a56141e75965
	wd:statement/Q947015-bb3ead7e-48d3-3083-4054-58afa28b5d7f
	wd:statement/Q947015-d7e3c5c4-4ab5-9475-add9-2874968b19da
p:P829	wd:statement/Q947015-7d843258-468c-826a-7390-44b557822d1a
p:direct-normalized/P508	<http://purl.org/bncf/tid/37200>
p:direct-normalized/P6366	<https://makg.org/entity/175432214>
wdt:P1343	Meyers Konversations-Lexikon, 4th edition (1885–1890)
wdt:P138	Leonhard Euler
wdt:P1889	Euler number
	Eulerian number
	Euler's number
wdt:P2534	"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>cosh</mi><mo>⁡</mo><mi>t</mi></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msup><mo stretchy="false">+</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mi>t</mi></mrow></mrow></msup></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">=</mo><mn>0</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">!</mo></mrow></mrow></mfrac></mrow><mo stretchy="false">⋅</mo><msup><mi>t</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P279	integer
wdt:P2812	"EulerNumber"
wdt:P31	integer sequence
	type of integer
wdt:P3417	"Euler-Number"
	"e-Eulers-Number"
wdt:P508	"37200"
wdt:P6104	WikiProject Mathematics
wdt:P6366	"175432214"
wdt:P646	"/m/0cn5v"
wdt:P7235	"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi mathvariant="normal">∞</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
	"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>n</mi><mo stretchy="false">!</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
	"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>t</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
	"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>cosh</mi><mo>⁡</mo><mi>t</mi></mrow></mrow></mfrac></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
	"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
	"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msup></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
	"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><munderover><mo form="prefix" stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">=</mo><mn>0</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P829	"A028296"

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