A new generalization of the Bernoulli and related polynomials

Abstract

In this paper, we introduce and investigate a generalization of the Bernoulli polynomials by means of a suitable generating function. We establish several interesting properties of these general polynomials. Furthermore, we give explicit series representations for these general polynomials in terms of a certain generalized Hurwitz-Lerch zeta function and the familiar Gauss hypergeometric function.