Euler Numbers and Polynomials Associated with Zeta Functions

Taekyun Kim

Abstract and Applied Analysis, 2008, vol. 2008, 1-11

Abstract:

For , the Euler zeta function and the Hurwitz-type Euler zeta function are defined by , and . Thus, we note that the Euler zeta functions are entire functions in whole complex -plane, and these zeta functions have the values of the Euler numbers or the Euler polynomials at negative integers. That is, , and . 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.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:581582

DOI: 10.1155/2008/581582

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