Some expansions for a class of generalized Humbert matrix polynomials

Abstract

The paper is an accomplishment of a new 3-variable 4-parameter generating function for Humbert matrix polynomials with an approach of unifying several classes of matrix valued polynomials using standard techniques of series manipulation. The results are contained in the form of explicit expression, hypergeometric matrix representation, generating functions and three additional expansions in nexus with Legendre, Hermite and Gegenbauer polynomials within discrete sections. A range of special cases is evenly traced that accounts due to the genuine wholesome generalization of such matrix polynomials.