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 Özden 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.