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1. INTRODUCTION The pseudo hyperbolic and pseudo trigonometric functions have been introduced on the eve of seventies by Ricci  in applications has been recognized only recently, within the context of problems involving arbitrary order coherent states [7, 13] and the emission of electromagnetic radiation by accelerated charges [7, 13]. This class of functions providing a fairly natural generalization of the ordinary exponential, hyperbolic and trigonometric functions [3, 4], offers the possibility of exploring, from a more general and unifying point of view, the theory of special functions including generalized cases. The pseudo-Laguerre, pseudo-Hermite polynomials and pseudo Bessel functions have been introduced in [5, 6]. Moreover, the Hermite matrix polynomials have been introduced and studied in [2, 10, 11, 12] for matrices in [C.sup.NxN] whose eigenvalues are all situated in the right open half-plane.