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

TL;DR

This paper introduces a new unified family of Apostol type-truncated exponential-Gould-Hopper polynomials, explores their properties through generating functions, and derives various identities and representations.

Contribution

It presents the first unified framework for these polynomials, including generating functions, operational properties, explicit formulas, and identities involving special functions.

Findings

Established generating functions for the unified polynomials

Derived explicit representations and multiplication formulas

Proved symmetric identities involving power sums and zeta functions

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.