On the Discrete q-Hermite Matrix Polynomials
Tóm tắt
There are two definitions for the discrete q-Hermite polynomials, one of them is defined for
$$01$$
. 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.
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