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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