An expansion formula for the Askey-Wilson function

DOI10.1006/jath.2001.3647zbMath0994.33009arXivmath/0105093OpenAlexW2048743549MaRDI QIDQ1604432

Jasper V. Stokman

Publication date: 4 July 2002

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0105093

zbMATH Keywords

Askey-Wilson polynomials\(q\)-difference operatorsAskey-Wilson function

Mathematics Subject Classification ID

Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Other transforms and operators of Fourier type (43A32) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items

Tensor products of $U^{\prime }_q\bigl (\widehat{sl}(2)\bigr )$Uq′sl̂(2)-modules and the big q2-Jacobi function transform, Multiple Askey–Wilson polynomials and related basic hypergeometric multiple orthogonal polynomials, A Paley-Wiener theorem for the Askey-Wilson function transform, Hyperbolic beta integrals, Wilson function transforms related to Racah coefficients, Koornwinder polynomials and the \(XXZ\) spin chain

Cites Work

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• One-dimensional double Hecke algebra and Gaussian sums
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• Some orthogonal very-well-poised \(_8\varphi_7\)-functions that generalize Askey-Wilson polynomials