An easy proof of the Askey-Wilson integral and applications of the method

DOI10.1006/jmaa.2000.6785zbMath0952.33004OpenAlexW1968446109MaRDI QIDQ1570217

Douglas Bowman

Publication date: 11 January 2001

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

Full work available at URL: https://doi.org/10.1006/jmaa.2000.6785

zbMATH Keywords

\(q\)-Hermite polynomialsAskey-Wilson integral\(q\)-Mehler formulaParseval theorem

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45)

Related Items (6)

\(q\)-difference equations for Askey-Wilson type integrals via \(q\)-polynomials ⋮ Bailey's well-poised \(_{6}\psi _{6}\)-series implies the Askey-Wilson integral ⋮ A multiple \(q\)-translation formula and its implications ⋮ A new proof of the Askey-Wilson integral via a five-variable Ramanujan's reciprocity theorem ⋮ Two expansion formulas involving the Rogers–Szegő polynomials with applications ⋮ Generalizations of Ramanujan's reciprocity formula and the Askey-Wilson integral

Cites Work

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• The combinatorics of q-Hermite polynomials and the Askey-Wilson integral
• A \(q\)-identity
• 𝑞-difference operators, orthogonal polynomials, and symmetric expansions
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• On the Askey-Wilson and Rogers Polynomials
• Convolutions of Orthonormal Polynomials
• Some Properties of the q-Hermite Polynomials
• q-Hermite Polynomials and Classical Orthogonal Polynomials
• Some polynomials related to theta functions

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