Expansions in the Askey-Wilson polynomials

DOI10.1016/j.jmaa.2014.11.048zbMath1309.33020OpenAlexW2114200871MaRDI QIDQ482000

Mourad E. H. Ismail, Dennis W. Stanton

Publication date: 19 December 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.11.048

zbMATH Keywords

generating functionsbasic hypergeometric seriesAskey-Wilson polynomialsAndrews formulaexpansion formulas

Mathematics Subject Classification ID

Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (8)

Formulas and identities involving the Askey-Wilson operator ⋮ Expansions in Askey-Wilson polynomials via Bailey transform ⋮ Bootstrapping and Askey-Wilson polynomials ⋮ Utility of integral representations for basic hypergeometric functions and orthogonal polynomials ⋮ Biorthogonal rational functions of $R_{II}$-type ⋮ The power collection method for connection relations: Meixner polynomials ⋮ On the Askey–Wilson polynomials and a $q$-beta integral ⋮ Convergence of spectral likelihood approximation based on q-Hermite polynomials for Bayesian inverse problems

Cites Work

• Bootstrapping and Askey-Wilson polynomials
• Connection relations and expansions
• \(q\)-orthogonal polynomials, Rogers-Ramanujan identities, and mock theta functions
• The combinatorics of q-Hermite polynomials and the Askey-Wilson integral
• Diagonalization of certain integral operators
• \(q\)-Taylor theorems, polynomial expansions, and interpolation of entire functions.
• Diagonalization of certain integral operators. II
• The special functions and their approximations. Vol. I, II
• Expansions of Hypergeometric Functions in Hypergeometric Functions
• Applications of q-Lagrange Inversion to Basic Hypergeometric Series
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• The Linearization of the Product of Continuous _q-Jacobi Polynomials
• Polynomial Expansions
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