On the q‐Extension of Apostol‐Euler Numbers and Polynomials

Young-Hee Kim, Wonjoo Kim and Lee-Chae Jang

Abstract and Applied Analysis, 2008, vol. 2008, issue 1

Abstract: Recently, Choi et al. (2008) have studied the q‐extensions of the Apostol‐Bernoulli and the Apostol‐Euler polynomials of order n and multiple Hurwitz zeta function. In this paper, we define Apostol′s type q‐Euler numbers En,q,ξ and q‐Euler polynomials En,q,ξ(x). We obtain the generating functions of En,q,ξ and En,q,ξ(x), respectively. We also have the distribution relation for Apostol′s type q‐Euler polynomials. Finally, we obtain q‐zeta function associated with Apostol′s type q‐Euler numbers and Hurwitz_s type q‐zeta function associated with Apostol′s type q‐Euler polynomials for negative integers.

Date: 2008
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https://doi.org/10.1155/2008/296159

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2008:y:2008:i:1:n:296159

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