A New Extension of Hermite-Hermite Matrix Polynomials and Their Properties

Ayman Shehata

Abstract

The main aim of this paper is to define and study of a new polynomial, say, two-index Hermite-Hermite matrix polynomials. An explicit representation, a matrix recurrence relation and matrix differential equations of these polynomials are presented. A new expansion of the matrix functions for a wide class of matrices in terms of two-index Hermite-Hermite matrix polynomials is proposed.