Michael J. Schlosser
A multidimensional generalization of Shukla's
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
very-well-poised 6Φ5 summation by
S. C. Milne,
a partial fraction decomposition, and analytic continuation.
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