Unified Apostol-Bernoulli, Euler and Genocchi polynomials

Abstract

In this paper, we present a unified family of polynomials including not only the Apostol-Bernoulli, Euler and Genocchi polynomials, but also a general family of polynomials suggested by Ozden et al. [H. Ozden, Y. Simsek, H.M. Srivastava, A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials. Comput. Math. Appl. 60 (10) (2010) 2779-2787]. We obtain the explicit representation of this unified family, in terms of a Gaussian hypergeometric function. Some symmetry identities and multiplication formula are also given. (C) 2011 Elsevier Ltd. All rights reserved.