Properties of some families of hypergeometric orthogonal polynomials in several variables

Details Properties of some families of hypergeometric orthogonal polynomials in several variables Properties of some families of hypergeometric orthogonal polynomials in several variables

1996-04-03

arxiv.org/abs/q-alg/9604004v1

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

Mathematics

Classical Analysis and ODEs

42 pages, AMSLaTeX 1.1 with amssymb

Scientific paper

10.1090/S0002-9947-99-02000-0

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 norms of the polynomials in terms of the norm of the constant polynomial.

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