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.