A Multidimensional Generalization of Shukla's 8ψ8 Summation |
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| Authors: | Schlosser |
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| Institution: | (1) Department of Mathematics The Ohio State University 231 West 18th Avenue Columbus, OH 43210 USA, US;(2) Institut für Mathematik der Universit?t Wien Strudlhofgasse 4 A-1090 Wien Austria schlosse@ap.univie.ac.at URL: http://www.mat.univie.ac.at/People/mschloss, AT |
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| Abstract: |
Abstract. We give an r -dimensional generalization of H. S. Shukla's very-well-poised
8
ψ
8
summation formula. We work in the setting of multiple basic hypergeometric series very-well-poised over the root system
A
r-1
or, equivalently, the unitary group U(r) . Our proof, which is already new in the one-dimensional case, utilizes an A
r-1
nonterminating very-well-poised
6
φ
5
summation by S. C. Milne, a partial fraction decomposition, and analytic continuation. |
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| Keywords: | , Basic hypergeometric series, q -Series, Bilateral series, 8ψ,8 Summation, 6φ,5 Summation, Ar Series, U\!(r) Series,,,,,,AMS Classification, Primary 33D15, Secondary 33D67, |
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