A study of ultraspherical matrix polynomials of two variables - Metwally M.S.; Shehata A. (Utilitas Mathematica, 2020)
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.