On the Discrete q-Hermite Matrix Polynomials

Abstract

There are two definitions for the discrete q-Hermite polynomials, one of them is defined for \(0 1\). This paper is devoted to extend these definitions to the discrete q-Hermite matrix polynomials by means of the generating matrix functions. Explicit expressions and Rodrigues-type formulas for the discrete q-Hermite matrix polynomials are obtained. Some recurrence relations for these matrix polynomials, in particular the three terms recurrence relations are given. Furthermore, some identities are proved.