A study of ultraspherical matrix polynomials of two variables

Abstract

The main aim of this paper is to define and study of the Ultraspherical matrix polynomials of two variables. An explicit representation, a three-term matrix recurrence relations and hypergeometric matrix representation for the Ultraspherical matrix polynomials of two variables are given. These polynomials appear as finite series solutions of a matrix partial differential equations and expansion of the Ultraspherical matrix polynomials as series of Hermite and Laguerre matrix polynomials of two variables are established. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.