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2008 Euler Numbers and Polynomials Associated with Zeta Functions
Taekyun Kim
Abstr. Appl. Anal. 2008: 1-11 (2008). DOI: 10.1155/2008/581582

Abstract

For s , the Euler zeta function and the Hurwitz-type Euler zeta function are defined by ζ E ( s ) = 2 n = 1 ( ( 1 ) n / n s ) , and ζ E ( s , x ) = 2 n = 0 ( ( 1 ) n / ( n + x ) s ) . Thus, we note that the Euler zeta functions are entire functions in whole complex s -plane, and these zeta functions have the values of the Euler numbers or the Euler polynomials at negative integers. That is, ζ E ( k ) = E k , and ζ E ( k , x ) = E k ( x ) . We give some interesting identities between the Euler numbers and the zeta functions. Finally, we will give the new values of the Euler zeta function at positive even integers.

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Taekyun Kim. "Euler Numbers and Polynomials Associated with Zeta Functions." Abstr. Appl. Anal. 2008 1 - 11, 2008. https://doi.org/10.1155/2008/581582

Information

Published: 2008
First available in Project Euclid: 9 September 2008

zbMATH: 1145.11019
MathSciNet: MR2407279
Digital Object Identifier: 10.1155/2008/581582

Rights: Copyright © 2008 Hindawi

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