An elliptic incarnation of the Bailey chain

An elliptic incarnation of the Bailey chain

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...

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Veröffentlicht in:International Mathematics Research Notices 2002, Vol.2002 (37), p.1945-1977
1. Verfasser: Spiridonov, V P
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container_end_page 1977
container_issue 37
container_start_page 1945
container_title International Mathematics Research Notices
container_volume 2002
creator Spiridonov, V P
description 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 10Φ9 basic hypergeometric series. An elliptic generalization of the Andrews-Berkovich 10Φ9 → 12Φ11 transformation formula is derived by employing an elliptic extension of a Bressoud's Bailey pair.
doi_str_mv 10.1155/S1073792802205127
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source Oxford University Press Journals All Titles (1996-Current)
title An elliptic incarnation of the Bailey chain
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