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Abstract and Applied Analysis
Volume 2008, Article ID 296159, 10 pages
Research Article

On the -Extension of Apostol-Euler Numbers and Polynomials

1Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, South Korea
2Natural Science Institute, KonKuk University, Chungju 380-701, South Korea
3Department of Mathematics and Computer Science, KonKuk University, Chungju 380-701, South Korea

Received 4 October 2008; Accepted 21 November 2008

Academic Editor: Lance Littlejohn

Copyright © 2008 Young-Hee Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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