1996/04/03 by J. F. van Diejen, Jan F. van Diejen · 63 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Algebra over a field #Askey–Wilson polynomials #Classical orthogonal polynomials #Difference polynomials #Discrete orthogonal polynomials #Gegenbauer polynomials #Generalization #Hahn polynomials #Hypergeometric distribution #Hypergeometric function #Jacobi polynomials #Koornwinder polynomials #Macdonald polynomials #Mathematical analysis #Mathematical functions and polynomials #Mathematics #Nonlinear Waves and Solitons #Orthogonal polynomials #Pure mathematics #Wilson polynomials #math.CA #math.QA #q-alg
paper · pdf · doi:10.1090/s0002-9947-99-02000-0
published in Transactions of the American Mathematical Society 351(1), 233-270 (American Mathematical Society) · 42 pages, AMSLaTeX 1.1 with amssymb
arxiv created 1996/04/03 · openalex publication_date 1999/01/01 · arxiv updated 2010/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.