\(U(n)\) very-well-poised \(_{10}\phi_ 9\) transformations
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.
scientific article; zbMATH DE number 908395
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