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Multilateral summation theorems for ordinary and basic hypergeometric series in U(n). (English) Zbl 0624.33012

In this paper we prove generalizations of \({}_ 2H_ 2\), \({}_ 5H_ 5\), \({}_ 1\Psi_ 1\), and \({}_ 6\Psi_ 6\) summation theorems for hypergeometric series in U(n). This includes a further generalization of Milne’s \({}_ 1\Psi_ 1\) summation theorem for basic hypergeometric series in U(n). These results are mostly obtained by use of contour integration together with Milne’s U(n) generalizations of the Gauss, \({}_ 5F_ 4\) and \({}_ 6\phi_ 5\) summation theorems.

MSC:

33C80 Connections of hypergeometric functions with groups and algebras, and related topics
33C05 Classical hypergeometric functions, \({}_2F_1\)
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