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Some Basic Extensions of Gustafson-Rakha's Multivariate Basic Hypergeometric Series
Medhat A. Rakha
Mathematics Department, Faculty of Science, Suez Canal University, Ismailia 41522, Egypt
marakha@hotmail.com
Annals of Combinatorics 6 (1) p.103-115 March, 2002
AMS Subject Classification: 33A15, 33A30, 33A65, 33A75
Abstract:
In this paper we extend some special cases of the multivariate basic hypergeometric series associated to the roots system of type that has been established and proved in [1]. For both types of the series, we will prove that when m=2n, n=1 one of the series is equivalent to Jackson's sum, while the other series is equivalent to the basic Gauss' sum.
Keywords: q-series, q-beta integrals, integral transformations, hypergeometric series very well poised on Lie algebras

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