Abstract
The main aim of this paper is to define a new polynomial, say, pseudo hyperbolic matrix functions, pseudo Hermite matrix polynomials and to study their properties. Some formulas related to an explicit representation, matrix recurrence relations are deduced, differential equations satisfied by them is presented, and the important role played in such a context by pseudo Hermite matrix polynomials are underlined. 2000 Mathematics Subject Classification. Primary 33C47: Secondary, 33-00, 33C45, 33E20, 35A22, 45P05, 47G10. Key words and phrases. Operational calculus, Pseudo hyperbolic functions, Hermite matrix polynomials, Matrix differential equation, Pseudo Hermite Polynomials.