Properties of some families of hypergeometric orthogonal polynomials in several variables

van Diejen, J.

doi:10.1090/S0002-9947-99-02000-0

Properties of some families of hypergeometric orthogonal polynomials in several variables
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by J. F. van Diejen PDF

Trans. Amer. Math. Soc. 351 (1999), 233-270 Request permission

Abstract:

Limiting cases are studied of the Koornwinder-Macdonald multivariable generalization of the Askey-Wilson polynomials. We recover recently and not so recently introduced families of hypergeometric orthogonal polynomials in several variables consisting of multivariable Wilson, continuous Hahn and Jacobi type polynomials, respectively. For each class of polynomials we provide systems of difference (or differential) equations, recurrence relations, and expressions for the (squared) norms of the polynomials in question.

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