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Zbl 0624.33012
Gustafson, R.A.
Multilateral summation theorems for ordinary and basic hypergeometric series in U(n). (English)
[J] SIAM J. Math. Anal. 18, 1576-1596 (1987). ISSN 0036-1410; ISSN 1095-7154/e

In this paper we prove generalizations of ${}\sb 2H\sb 2$, ${}\sb 5H\sb 5$, ${}\sb 1\Psi\sb 1$, and ${}\sb 6\Psi\sb 6$ summation theorems for hypergeometric series in U(n). This includes a further generalization of Milne's ${}\sb 1\Psi\sb 1$ 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, ${}\sb 5F\sb 4$ and ${}\sb 6\phi\sb 5$ summation theorems.

MSC 2000:: *33C80 Connections of theory of special functions with groups and algebras
33C05 Classical hypergeometric functions

Keywords: hypergeometric series in U(n); summation theorems; basic hypergeometric series; contour integration

Cited in: Zbl 1023.33013

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