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

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

2003-04-18

arxiv.org/abs/math/0304249v2

Indag. Math. (N.S.) 14 (2003), 483-514

Mathematics

Classical Analysis and ODEs

29 pages, minor changes; to appear in Indag. Math., special volume dedicated to Tom Koornwinder

Scientific paper

Using multiple q-integrals and a determinant evaluation, we establish a multivariable extension of Bailey's nonterminating 10-phi-9 transformation. From this result, we deduce new multivariable terminating 10-phi-9 transformations, 8-phi-7 summations and other identities. We also use similar methods to derive new multivariable 1-psi-1 summations. Some of our results are extended to the case of elliptic hypergeometric series.

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