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2008 On the q -Extension of Apostol-Euler Numbers and Polynomials
Young-Hee Kim, Wonjoo Kim, Lee-Chae Jang
Abstr. Appl. Anal. 2008: 1-10 (2008). DOI: 10.1155/2008/296159

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 E n , q , ξ and q -Euler polynomials E n , q , ξ ( x ) . We obtain the generating functions of E n , q , ξ and E n , 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.

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Young-Hee Kim. Wonjoo Kim. Lee-Chae Jang. "On the q -Extension of Apostol-Euler Numbers and Polynomials." Abstr. Appl. Anal. 2008 1 - 10, 2008. https://doi.org/10.1155/2008/296159

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Published: 2008
First available in Project Euclid: 10 February 2009

zbMATH: 1247.11028
MathSciNet: MR2466221
Digital Object Identifier: 10.1155/2008/296159

Rights: Copyright © 2008 Hindawi

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