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Some relations satisfied by orthogonal matrix polynomials. (English) Zbl 1229.33012

Summary: The main purpose of this paper is to obtain some properties of orthogonal matrix polynomials. We derive identities for power series satisfied by Laguerre, Hermite and Gegenbauer matrix polynomials. Furthermore, for these matrix polynomials, we give raising operators.

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
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