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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 2 H 2 , 5 H 5 , 1 Ψ 1 , and 6 Ψ 6 summation theorems for hypergeometric series in U(n). This includes a further generalization of Milne’s 1 Ψ 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, 5 F 4 and 6 ϕ 5 summation theorems.

33C80Connections of hypergeometric functions with groups and algebras
33C05Classical hypergeometric functions, 2 F 1