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Recurrences for elliptic hypergeometric integrals

Rains, Eric M. (2005) Recurrences for elliptic hypergeometric integrals. . (Submitted)

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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.

Item Type:Report or Paper (Discussion Paper)
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Record Number:CaltechAUTHORS:20171009-142453684
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82226
Deposited By: Tony Diaz
Deposited On:09 Oct 2017 21:42
Last Modified:03 Oct 2019 18:52

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