Published October 9, 2017
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Recurrences for elliptic hypergeometric integrals
- Creators
- Rains, Eric M.
Abstract
In recent work (math.QA/0309252) on multivariate hypergeometric integrals, the author generalized a conjectural integral formula of van Diejen and Spiridonov to a ten parameter integral provably invariant under an action of the Weyl group E_7. In the present note, we consider the action of the affine Weyl group, or more precisely, the recurrences satisfied by special cases of the integral. These are of two flavors: linear recurrences that hold only up to dimension 6, and three families of bilinear recurrences that hold in arbitrary dimension, subject to a condition on the parameters. As a corollary, we find that a codimension one special case of the integral is a tau function for the elliptic Painlevé equation.
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Additional details
- Eprint ID
- 82226
- Resolver ID
- CaltechAUTHORS:20171009-142453684
- Created
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2017-10-09Created from EPrint's datestamp field
- Updated
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2023-06-01Created from EPrint's last_modified field