A new proof of the Askey-Wilson integral via a five-variable Ramanujan's reciprocity theorem

DOI10.1007/s11139-010-9221-xzbMath1207.05019OpenAlexW2047467512MaRDI QIDQ631491

Xin Rong Ma

Publication date: 14 March 2011

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

Full work available at URL: https://doi.org/10.1007/s11139-010-9221-x

zbMATH Keywords

\(q\)-seriesRamanujan's reciprocity theoremAskey-Wilson integral\(q\)-beta integral

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) (q)-gamma functions, (q)-beta functions and integrals (33D05)

Related Items (1)

Askey-Wilson integral and its generalizations

Cites Work

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• An elementary evaluation of a beta type integral
• Askey-Wilson type integrals associated with root systems
• Six-variable generalization of Ramanujan's reciprocity theorem and its variants
• An identity of Andrews and the Askey-Wilson integral
• The combinatorics of q-Hermite polynomials and the Askey-Wilson integral
• Ramanujan's ``lost notebook. I: Partial Theta-functions
• An easy proof of the Askey-Wilson integral and applications of the method
• Some operator identities and \(q\)-series transformation formulas
• A reciprocity theorem for certain \(q\)-series found in Ramanujan's lost notebook
• A Simple Evaluation of Askey and Wilson's q-Beta Integral
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• A q-EXTENSION OF CAUCHY'S FORM OF THE BETA INTEGRAL
• Generalizations of Ramanujan's reciprocity theorem and their applications
• Ramanujan's Lost Notebook

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