Michael J. Schlosser

A multidimensional generalization of Shukla's 8Ψ8 summation

(16 pages)

Abstract. We give an r-dimensional generalization of H. S. Shukla's very-well-poised 8Ψ8 summation formula. We work in the setting of multiple basic hypergeometric series very-well-poised over the root system Ar-1, or equivalently, the unitary group U(r). Our proof, which is already new in the one-dimensional case, utilizes an Ar-1 nonterminating very-well-poised 6Φ5 summation by S. C. Milne, a partial fraction decomposition, and analytic continuation.

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