A new class of generalized Apostol–Bernoulli polynomials and some analogues of the Srivastava–Pintér addition theorem

Abstract

The main purpose of this paper is to introduce and investigate a new class of generalized Apostol–Bernoulli polynomials based on a definition given by Natalini and Bernardini (2003) [22] for the generalized Bernoulli polynomials. We obtain a generalization of the Srivastava–Pintér addition theorem (Srivastava and Pintér (2004) [23]). We also give a list of expressions involving special functions that could be used to obtain some analogues of the Srivastava–Pintér addition theorem. Finally, we give an analogue featuring the new class of generalized Apostol–Bernoulli polynomials.