\(U(n)\) very-well-poised \(_{10}\phi_ 9\) transformations
type: Item
instance of: scholarly article
title: \(U(n)\) very-well-poised \(_{10}\phi_ 9\) transformations
zbMATH Open document ID: 0870.33013
DOI: 10.1016/0377-0427(95)00248-0
author: Stephen C. Milne
author: John W. Newcomb
published in: Journal of Computational and Applied Mathematics
publication date: 1997-09-08T00:00:00Z
review text: Building up upon previous work by Milne and Lilly, the authors derive extensions of Bailey's classical very-well-poised \(_{10} \Phi_9\)-transformations to multiple basic hypergeometric series associated to root system \(A_n\) (which is synonymous to ``\(U (n+1)\) basic hypergeometric series''). Limiting cases include \(U(n+1)\) extensions of Watson's \(_8\Phi_7\)-to-\(_4\varphi_3\)-transformation formula, of Sears' balanced \(_4\Phi_3\)-transformation formula of classical two-term \(_3\Phi_2\)-transformation formulas, and of the nonterminating very-well-poised \(_8\Phi_7\)-transformation formulas. A previously given \(U (n+1)\)-extension of the \(_{10} \Phi_9\)-transformation formula of \textit{R. Y. Denis} and \textit{R. A. Gustafson} [SIAM J. Math. Anal. 23, No. 2, 552-561 (1992; Zbl 0777.33009)] is a special case of one of the identities in this paper.
Mathematics Subject Classification ID: 33D80
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 05A30
Mathematics Subject Classification ID: 33D20
zbMATH DE Number: 908395
zbMATH Keywords: root systems
zbMATH Keywords: basic hypergeometric series
reviewed by: C. Krattenthaler
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00248-0
OpenAlex ID: W2043882816
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description: scientific article; zbMATH DE number 908395