An extension of Askey-Wilson's \(q\)-beta integral and its applications
type: Item
instance of: scholarly article
title: An extension of Askey-Wilson's \(q\)-beta integral and its applications
zbMATH Open document ID: 0760.33010
author: S. Singh
published in: Rocky Mountain Journal of Mathematics
publication date: 1993-01-17T00:00:00Z
review text: In this interesting paper the authors prove several further extensions of the familiar \(q\)-beta integral evaluated earlier by \textit{R. Askey} and \textit{J. A. Wilson} [Mem. Am. Math. Soc. 319, 1-55 (1985; Zbl 0572.33012)]. They also exhibit connections of their results with various known results given recently in the theory of basic hypergeometric series. The transformation and integral formulas, derived systematically in this paper, are much too involved to be reproduced in this review.
Mathematics Subject Classification ID: 33D90
zbMATH DE Number: 97441
zbMATH Keywords: \(q\)-beta integral
reviewed by: H. M. Srivastava
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072764
OpenAlex ID: W2028943113
cites work: Some Transformations of Well-Poised Basic Hypergeometric Series of the Type 8 Φ 7
cites work: Some Remarks on q-Beta Integral
cites work: Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
cites work: The combinatorics of q-Hermite polynomials and the Askey-Wilson integral
cites work: Projection Formulas, a Reproducing Kernel and a Generating Function for q-Wilson Polynomials
cites work: A q-analogue of Appell's \(F_ 1\) function and some quadratic transformation formulas for non-terminating basic hypergeometric series
cites work: Transformations between basic hypergeometric series on different bases and identities of Rogers-Ramanujan type
cites work: Transformations of non-terminating basic hypergeometric series, their contour integrals and applications to Rogers-Ramanujan identites
DOI: 10.1216/RMJM/1181072764
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description: scientific article; zbMATH DE number 97441