On Matrix polynomials associated with Hermite polynomials

Abstract

In this paper, an extension of the Hermite matrix polynomials is introduced. Some relevant matrix functions appear in terms of the two-index and two-variable and p-index and p-variable Hermite matrix polynomials. Furthermore, in order to give qualitative properties of this family of matrix polynomials, the Legendre and Chebyshev matrix polynomials of sveral variables are introduced.