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Heine transformations for a new kind of basic hypergeometric series in \(U(n)\). (English) Zbl 0853.33015

Summary: Heine transformation are proved for a new kind of multivariate basic hypergeometric series which had been previously introduced by Krattenthaler in connection with generating functions for nonintersecting lattice paths. As a consequence, a \(q\)-Gauss and \(q\)-Chu-Vandermonde sum are proved and also a generalization of Ramanujan’s \(_1 \psi_2\) sum.

MSC:

33D80 Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics
33D70 Other basic hypergeometric functions and integrals in several variables
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