Gustafson, R. A. Multilateral summation theorems for ordinary and basic hypergeometric series in U(n). (English) Zbl 0624.33012 SIAM J. Math. Anal. 18, 1576-1596 (1987). 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. Cited in 1 ReviewCited in 29 Documents MSC: 33C80 Connections of hypergeometric functions with groups and algebras, and related topics 33C05 Classical hypergeometric functions, \({}_2F_1\) Keywords:hypergeometric series in U(n); summation theorems; basic hypergeometric series; contour integration PDFBibTeX XMLCite \textit{R. A. Gustafson}, SIAM J. Math. Anal. 18, 1576--1596 (1987; Zbl 0624.33012) Full Text: DOI Digital Library of Mathematical Functions: §17.15 Generalizations ‣ Properties ‣ Chapter 17 𝑞-Hypergeometric and Related Functions