On $BC$ type basic hypergeometric orthogonal polynomials

DOI10.1090/S0002-9947-99-02551-9zbMath0936.33008arXivq-alg/9707005OpenAlexW1626773039MaRDI QIDQ4942849

Jasper V. Stokman

Publication date: 15 March 2000

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9707005

zbMATH Keywords

Koornwinder polynomialsresidue calculusmultivariable basic hypergeometric orthogonal polynomials\(q\)-Selberg type integralsmultivariable \(q\)-Racah polynomialsmultivariable big and little \(q\)-Jacobi polynomials

Mathematics Subject Classification ID

Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items

Charting the 𝑞-Askey scheme, Some systems of multivariable orthogonal \(q\)-Racah polynomials, Askey-Wilson type integrals associated with root systems, Spin chains and Gustafson’s integrals, A bilateral extension of the $q$-Selberg integral, On Gustafson integrals for the group \(\mathrm{SL}(2,\mathbb{R} )\), Mellin-Barnes integrals related to the Lie algebra \(u(N)\), Elliptic beta integrals and modular hypergeometric sums: An overview., The importance of the Selberg integral, Elliptic hypergeometric series on root systems., Symmetric and nonsymmetric Koornwinder polynomials in the \(q \to 0\) limit, \(\mathrm{SL}(2,\mathbb{C})\) Gustafson integrals, Macdonald-level extension of beta ensembles and large-\(N\) limit transition, On complex gamma-function integrals, On some limit cases of Askey-Wilson polynomials, Elements of the q-Askey scheme in the algebra of symmetric functions, On a Selberg-Schur integral, \(q\)-Selberg integrals and Koornwinder polynomials

Cites Work

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• Multivariable Al-Salam & Carlitz Polynomials Associated with the TypeA q-Dunkl Kernel
• Self-dual Koornwinder-Macdonald polynomials
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