On Pseudo Hermite Matrix Polynomials of Two Variables (Report‪)‬

1. INTRODUCTION The pseudo hyperbolic and pseudo trigonometric functions have been introduced on the eve of seventies by Ricci [14] 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.