Families of Generating Functions for the Jacobi and Related Matrix Polynomials

Abstract

The Jacobi matrix polynomials and their orthogonality only for commutative matrices was first studied by Defez \(et. al\).
[Jacobi matrix differential equation, polynomial solutions and their properties. Comput. Math. Appl. \(48 (2004), 789-803]\). It is known that orthogonal matrix polynomials comprise an emerging field of study, with important results in both theory and applications continuing to appear in the literature. The main object of this paper is to derive various families of linear, multilateral and multilinear generating functions for the Jacobi matrix polynomials and the Gegenbauer matrix polynomials. Recurrence relations of Jacobi matrix polynomials are obtained. Some special cases of the results presented in this study are also indicated.