On generalized two-index Hermite matrix polynomials

In this study, we give a new generalization for Hermite matrix polynomials. We obtain some formulas related to an explicit representation, matrix recurrence relations and the Rodrigues formula for two-index Hermite matrix polynomials. Also we generalize Runge's addition formula and Nielsen's identity for these new generalizations. Moreover we give Burchnall's operational formula and Nielsen's identity for Hermite matrix polynomials by means of two-index Hermite matrix polynomials.