A multidimensional generalization of Shukla's 8-psi-8 summation

Abstract

We give an r-dimensional generalization of H. S. Shukla's very-well-poised 8-psi-8 summation formula. We work in the setting of multiple basic hypergeometric series very-well-poised over the root system A_{r-1}, or equivalently, the unitary group U(r). Our proof, which is already new in the one-dimensional case, utilizes an A_{r-1} nonterminating very-well-poised 6-phi-5 summation by S. C. Milne, a partial fraction decomposition, and analytic continuation.