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On a multivariable extension of Jacobi matrix polynomials. (English) Zbl 1221.33022

Summary: The classical Jacobi matrix polynomials only for commutative matrices were first studied by E. Defez, L. Jódar and A. Law [Comput. Math. Appl. 48, No. 5–6, 789–803 (2004; Zbl 1069.33007)]. The main aim of this paper is to construct a multivariable extension with the help of the classical Jacobi matrix polynomials (JMPs). Generating matrix functions and recurrence relations satisfied by these multivariable matrix polynomials are derived. Furthermore, general families of multilinear and multilateral generating matrix functions are obtained and their applications are presented.

MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
15B57 Hermitian, skew-Hermitian, and related matrices

Citations:

Zbl 1069.33007
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