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An \(SU(n)q\)-beta integral transformation and multiple hypergeometric series identities. (English) Zbl 0777.33009

The authors prove two very general results. The first is an \(SU(n)\) multivariate integral transformation that generalizes W. N. Bailey’s very well poised \(_{10}\phi_ 9\) transformation. This is first proved as an integral transformation. The corresponding series transformation is then derived from it. The second result is an \(Sp(n)\) generalization of F. H. Jackson’s very well poised \(_ 8\phi_ 7\) summation.

MSC:

33D05 \(q\)-gamma functions, \(q\)-beta functions and integrals
33D80 Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics
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