Certain results for unified Apostol type-truncated exponential-Gould-Hopper polynomials and their relatives

Abstract

The present article aims to introduce a unified family of the Apostol type-truncated exponential-Gould-Hopper polynomials and to characterize its properties via generating functions. A unified presentation of the generating function for the Apostol type-truncated exponential-Gould-Hopper polynomials is established and its applications are given. By the use of operational techniques, the quasi-monomial properties for the unified family are proved. Several explicit representations and multiplication formulas related to these polynomials are obtained. Some general symmetric identities involving multiple power sums and Hurwitz-Lerch zeta functions are established by applying different analytical means on generating functions.