Certain hybrid polynomials associated with Sheffer sequences

TL;DR

This paper introduces new hybrid polynomials linked to Sheffer sequences, unifying and generalizing various polynomial families through operational methods and generating functions.

Contribution

It develops a framework using operational methods to unify and generalize new and existing polynomials related to Sheffer sequences and Legendre-Gould Hopper polynomials.

Findings

Derived properties of the new polynomials

Unified various polynomial families

Provided easy derivations of known and new polynomials

Abstract

Inspired by the framework of operational methods and based on the generating functions of Legendre-Gould Hopper polynomials and Sheffer sequences, we discuss certain new mixed type polynomials and their important properties. We show that the use of operational nature allows the relevant polynomials to be unified and general in nature. It is illustrated how the polynomials, we develop, provide an easy derivation of a wide class of new and known polynomials, and their respective properties.