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- Euler_number abstract "In number theory, the Euler numbers are a sequence En of integers (sequence A122045 in OEIS) defined by the following Taylor series expansion:where cosh t is the hyperbolic cosine. The Euler numbers appear as a special value of the Euler polynomials.The odd-indexed Euler numbers are all zero. The even-indexed ones (sequence A028296 in OEIS) have alternating signs. Some values are:E0 = 1E2 = −1E4 = 5E6 = −61E8 = 1,385E10 = −50,521E12 = 2,702,765E14 = −199,360,981E16 = 19,391,512,145E18 = −2,404,879,675,441Some authors re-index the sequence in order to omit the odd-numbered Euler numbers with value zero, and/or change all signs to positive. This encyclopedia adheres to the convention adopted above.The Euler numbers appear in the Taylor series expansions of the secant and hyperbolic secant functions. The latter is the function in the definition. They also occur in combinatorics, specifically when counting the number of alternating permutations of a set with an even number of elements.".
- Euler_number wikiPageID "46895".
- Euler_number wikiPageRevisionID "605001421".
- Euler_number hasPhotoCollection Euler_number.
- Euler_number id "p/e036540".
- Euler_number title "Euler number".
- Euler_number title "Euler numbers".
- Euler_number urlname "EulerNumber".
- Euler_number subject Category:Integer_sequences.
- Euler_number type Abstraction100002137.
- Euler_number type Arrangement107938773.
- Euler_number type Group100031264.
- Euler_number type IntegerSequences.
- Euler_number type Ordering108456993.
- Euler_number type Sequence108459252.
- Euler_number type Series108457976.
- Euler_number comment "In number theory, the Euler numbers are a sequence En of integers (sequence A122045 in OEIS) defined by the following Taylor series expansion:where cosh t is the hyperbolic cosine. The Euler numbers appear as a special value of the Euler polynomials.The odd-indexed Euler numbers are all zero. The even-indexed ones (sequence A028296 in OEIS) have alternating signs.".
- Euler_number label "Euler number".
- Euler_number label "Eulergetal (getaltheorie)".
- Euler_number label "Eulersche Zahlen".
- Euler_number label "Nombre d'Euler".
- Euler_number label "Numero di Eulero (teoria dei numeri)".
- Euler_number label "Número de Euler".
- Euler_number label "عدد أويلر".
- Euler_number label "オイラー数".
- Euler_number label "欧拉数".
- Euler_number sameAs Eulersche_Zahlen.
- Euler_number sameAs Número_de_Euler.
- Euler_number sameAs Nombre_d'Euler.
- Euler_number sameAs Numero_di_Eulero_(teoria_dei_numeri).
- Euler_number sameAs オイラー数.
- Euler_number sameAs 오일러_수.
- Euler_number sameAs Eulergetal_(getaltheorie).
- Euler_number sameAs m.0cn5v.
- Euler_number sameAs Q947015.
- Euler_number sameAs Q947015.
- Euler_number sameAs Euler_number.
- Euler_number wasDerivedFrom Euler_number?oldid=605001421.
- Euler_number isPrimaryTopicOf Euler_number.