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Properties of some families of hypergeometric orthogonal polynomials in several variables


Author: J. F. van Diejen
Journal: Trans. Amer. Math. Soc. 351 (1999), 233-270
MSC (1991): Primary 33C50; Secondary 33D45
DOI: https://doi.org/10.1090/S0002-9947-99-02000-0
MathSciNet review: 1433128
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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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Additional Information

J. F. van Diejen
Affiliation: Department of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153, Japan
Address at time of publication: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago 1, Chile

DOI: https://doi.org/10.1090/S0002-9947-99-02000-0
Keywords: Orthogonal polynomials in several variables, difference and differential equations, recurrence relations, orthonormalization constants, Selberg type integrals, quantum integrable $n$-particle systems
Received by editor(s): April 8, 1996
Received by editor(s) in revised form: November 25, 1996
Additional Notes: Work supported by the Japan Society for the Promotion of Science (JSPS) and by a Monbusho Grant-in-Aid.
Article copyright: © Copyright 1999 American Mathematical Society

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