### Annals of Combinatorics 4 (2000) 347-373

q-Beta Integrals and Multivariate Basic Hypergeometric Series Associated to Root Systems of Type Am

Robert A. Gustafson and Medhat A. Rakha

Department of Mathematics, Texas A & M University, College Station, Texas 77843, USA
robert.gustafson@math.tamu.edu

Department of Mathematics, Faculty of Science, Suez Canal University, Ismailia - 41522, Egypt
mrakha@ismailia.ie-eg.com

AMS Subject Classification: 33A15, 33A30, 33A65, 33A75

Abstract. In this paper we establish and prove two new q-beta integrals and two multivariate basic hypergeometric series associated to the root system of Am. We give a generalization of Jackson's well-poised  sum for one kind of series and a generalization of the q-Gauss sum for the other kind of series.

Keywords: q-series, q-beta integrals, integral transformations, hypergeometric series well poised on Lie algebras

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