Recurrences for elliptic hypergeometric integrals

Details Recurrences for elliptic hypergeometric integrals Recurrences for elliptic hypergeometric integrals

2005-04-13

arxiv.org/abs/math/0504285v1

Mathematics

Classical Analysis and ODEs

16 pages LaTeX. From workshop on Elliptic Integrable Systems, RIMS 11/2004

Scientific paper

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 Painlev\'e equation.

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