Nonterminating q-whipple transformations for basic hypergeometric series in U(n)

Abstract

In this paper we derive multivariable generalizations of Bailey's classical nonterminating q-Whipple and q-Saalschütz transformations.We work in the setting of multiple basic hypergeometric series very-well-poised on unitary groups U(n+1), multiple series that are associated to the root system A n. We extend Bailey's proofs of these transformations by first taking suitable limits of our U(n+1) 10φ 9 transformation formula, in which the multiple sums are taken over an n-dimensional tetrahedron (n-simplex). A natural partition of the (finite) n-simplex combines with our analysis of the convergence of the multiple series to yield our transformations. We expect that all of these results will directly extend to the analogous case of multiple basic hypergeometric series associated to the root system D n. © Springer Science+Business Media, LLC 2012.