Formulas and identities involving the Askey-Wilson operator

DOI10.1016/j.aam.2016.02.002zbMath1336.33026OpenAlexW2290514094MaRDI QIDQ272896

Mourad E. H. Ismail, Plamen C. Simeonov

Publication date: 21 April 2016

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2016.02.002

zbMATH Keywords

generating functiontransformationintegration by partsbasic hypergeometric seriesAskey-Wilson operatorAskey-Wilson polynomialCooper's formulaRodriguez formulasummation theorem

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (4)

On a generalization of the Rogers generating function ⋮ Divided differences and well-poised q-series ⋮ The power collection method for connection relations: Meixner polynomials ⋮ Connection relations for \(q\)-Taylor polynomial bases

Cites Work

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• Bootstrapping and Askey-Wilson polynomials
• Expansions in the Askey-Wilson polynomials
• Connection relations and expansions
• \(q\)-Taylor and interpolation series for Jackson \(q\)-difference operators
• The combinatorics of q-Hermite polynomials and the Askey-Wilson integral
• The classical moment problem as a self-adjoint finite difference operator
• \(q\)-Taylor theorems, polynomial expansions, and interpolation of entire functions.
• Some operator identities and \(q\)-series transformation formulas
• On the $q$-partial differential equations and $q$-series
• An extension of the non-terminating₆φ₅summation and the Askey–Wilson polynomials
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• The Askey–Wilson polynomials and q-Sturm–Liouville problems

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