ELA, Volume 10, pp. 272-279, November 2003, abstract.

On Generalized Hermite Matrix Polynomials

K.A.M. Sayyed, M.S. Metwally and R.S. Batahan

In this paper a new generalization of the Hermite 
matrix polynomials is given. An explicit representation 
and an expansion of the matrix exponential in a series 
of these matrix polynomials is obtained. Some recurrence 
relations, in particular the three terms recurrence 
relation, are given for these matrix polynomials. It is 
proved that the generalized Hermite matrix polynomials 
satisfy a matrix differential equation.