Multivariable Askey-Wilson function and bispectrality

DOI10.1007/s11139-010-9244-3zbMath1221.33031OpenAlexW2000006488MaRDI QIDQ539125

Jeffrey S. Geronimo, Plamen Iliev

Publication date: 27 May 2011

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-010-9244-3

zbMATH Keywords

hypergeometric seriesbispectralitymultivariable orthogonal polynomials

Mathematics Subject Classification ID

Difference operators (39A70) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable (33D50)

Related Items (10)

\(3nj\)-symbols and identities for \(q\)-Bessel functions ⋮ A bivariate \(Q\)-polynomial structure for the non-binary Johnson scheme ⋮ Representations of the rank two Racah algebra and orthogonal multivariate polynomials ⋮ Coupling coefficients of \(\operatorname{su}_{q}(1,1)\) and multivariate \(q\)-Racah polynomials ⋮ Linear partial \(q\)-difference equations on \(q\)-linear lattices and their bivariate \(q\)-orthogonal polynomial solutions ⋮ Linear Partial Divided-Difference Equation Satisfied by Multivariate Orthogonal Polynomials on Quadratic Lattices ⋮ Bispectral extensions of the Askey-Wilson polynomials ⋮ Hypergeometric Multivariate Orthogonal Polynomials ⋮ A bispectral q-hypergeometric basis for a class of quantum integrable models ⋮ Koornwinder polynomials and the \(XXZ\) spin chain

Cites Work

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• Differential equations in the spectral parameter
• Askey-Wilson type functions with bound states
• Discrete orthogonal polynomials and difference equations of several variables
• Bispectrality of multivariable Racah-Wilson polynomials
• Orthogonal polynomials associated with root systems
• Nonsymmetric Koornwinder polynomials and duality
• Macdonald's evaluation conjectures and difference Fourier transform
• Some systems of multivariable orthogonal \(q\)-Racah polynomials
• Bispectral commuting difference operators for multivariable Askey-Wilson polynomials
• Some Systems of Multivariable Orthogonal Askey-Wilson Polynomials
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• The Associated Askey-Wilson Polynomials
• Some multivariable orthogonal polynomials of the Askey tableau—Continuous families
• Some multivariable orthogonal polynomials of the Askey tableau-discrete families
• Some orthogonal very well poised -functions
• A Multi-dimensional Linear Growth Birth and Death Process
• Some orthogonal very-well-poised \(_8\varphi_7\)-functions that generalize Askey-Wilson polynomials
• Self-dual Koornwinder-Macdonald polynomials

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