A note on Hermite matrix based Narumi polynomials

Abstract

In this article, the 2-index 2-variable Hermite matrix based Narumi polynomials are introduced by means of generating function. Some important properties including operational representation and quasi-monomiality of these polynomials are established. For suitable values of indices and variables, the 2-index 2-variable Hermite matrix polynomials yield several special matrix polynomials. Consequently, the results for the corresponding new special polynomials related to Narumi polynomials are presented.