Finding hybrid families of special matrix polynomials associated with Sheffer sequences

Abstract

In this paper, three index three variable Hermite matrix based Sheffer polynomials (3I3VHMSP) are introduced by algebraic decomposition of exponential operators. The operational methods combined with the monomiality principle can be used to introduce 3I3VHMSP and also to establish rules of operational nature, framing the special polynomials within the context of particular solutions of generalized forms of partial differential equations of evolution type. The Appell and Sheffer sequences along with the operational formalism offer a powerful tool for investigation of the properties of a wide class of polynomials. Further, operational representation providing connections between 3I3VHMSP families and the known special polynomials are established, which are used to derive new identities and the results for the members of these new families. The approach presented is general.