Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 451217, 12 pages
doi:10.1155/2009/451217
Research Article

Interpolation Functions of q-Extensions of Apostol's Type Euler Polynomials

Kyung-Won Hwang,1 Young-Hee Kim,2 and Taekyun Kim2

1Department of General Education, Kookmin University, Seoul 136-702, South Korea
2Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, South Korea

Received 16 May 2009; Accepted 25 July 2009

Academic Editor: Vijay Gupta

Copyright © 2009 Kyung-Won Hwang 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.

Abstract

The main purpose of this paper is to present new q-extensions of Apostol's type Euler polynomials using the fermionic p-adic integral on ℤp. We define the q-λ-Euler polynomials and obtain the interpolation functions and the Hurwitz type zeta functions of these polynomials. We define q-extensions of Apostol type's Euler polynomials of higher order using the multivariate fermionic p-adic integral on ℤp. We have the interpolation functions of these q-λ-Euler polynomials. We also give (h,q)-extensions of Apostol's type Euler polynomials of higher order and have the multiple Hurwitz type zeta functions of these (h,q)-λ-Euler polynomials.