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An elliptic incarnation of the Bailey chain. (English) Zbl 1185.33023
Summary: For the first time a Bailey chain with all entries composed out of the Jacobi theta functions is constructed. This is an elliptic extension of the WP (well-poised) Bailey chain of Andrews and it generates an infinite sequence of identities for theta hypergeometric series. As a particular example, we obtained a new proof of the Frenkel-Turaev elliptic analogue of the Bailey transformation for a terminating 10 Φ 9 basic hypergeometric series. An elliptic generalization of the Andrews-Berkovich 10 Φ 9 12 Φ 11 transformation formula is derived by employing an elliptic extension of a Bressoud’s Bailey pair.
MSC:
33D15Basic hypergeometric functions of one variable, r φ s
33E05Elliptic functions and integrals