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Families of generating functions for the Jacobi and related matrix polynomials. (English) Zbl 1340.33007

Summary: The Jacobi matrix polynomials and their orthogonality only for commutative matrices were first studied by E. Defez et al. [Comput. Math. Appl. 48, No. 5–6, 789–803 (2004; Zbl 1069.33007)]. 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.

MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory

Citations:

Zbl 1069.33007
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