Some applications of the Hermite matrix polynomials series expansions

This paper deals with Hermite matrix polynomials expansions of some relevant matrix functions appearing in the solution of differential systems. Properties of Hermite matrix polynomials such as the three terms recurrence formula permit an efficient computation of matrix functions avoiding important computational drawbacks of other well-known methods. Results are applied to compute accurate approximations of certain differential systems in terms of Hermite matrix polynomials.