Limits of multivariate elliptic beta integrals and related bilinear forms

Details Limits of multivariate elliptic beta integrals and related bilinear forms Limits of multivariate elliptic beta integrals and related bilinear forms

2011-10-07

arxiv.org/abs/1110.1460v1

Mathematics

Classical Analysis and ODEs

31 pages. This is part 3 of a 3 part series on limits of multivariate biorthogonal elliptic hypergeometric series. This part i

Scientific paper

In this article we consider the elliptic Selberg integral, which is a BC_n symmetric multivariate extension of the elliptic beta integral. We categorize the limits that are obtained as p->0, for given behavior of the parameters as p->0. This article is therefore the multivariate version of our earlier paper "Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions". The integrand of the elliptic Selberg integral is the measure for the BC_n symmetric biorthogonal functions introduced by the second author, so we also consider the limits of the associated bilinear form. We also provide the limits for the discrete version of this bilinear form, which is related to a multivariate extension of the Frenkel-Turaev summation.

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