Hjalmar Rosengren and Michael J. Schlosser

Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations

(29 pages)

Abstract. Using multiple q-integrals and a determinant evaluation, we establish a multivariable extension of Bailey's nonterminating 10φ9 transformation. From this result, we deduce new multivariable terminating 10φ9 transformations, 8φ7 summations and other identities. We also use similar methods to derive new multivariable 1ψ1 summations. Some of our results are extended to the case of elliptic hypergeometric series.

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