Limits of multivariate elliptic beta integrals and related bilinear forms
@article{Bult2011LimitsOM, title={Limits of multivariate elliptic beta integrals and related bilinear forms}, author={Fokko J. van de Bult and Eric M. Rains}, journal={arXiv: Classical Analysis and ODEs}, year={2011} }
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…
6 Citations
Limits of multivariate elliptic hypergeometric biorthogonal functions
- Mathematics
- 2011
In this article we extend the results of our article "Limits of elliptic hypergeometric biorthogonal functions" to the multivariate setting. In that article we determined which families of…
Elliptic Combinatorics and Markov Processes
- Mathematics
- 2012
We present combinatorial and probabilistic interpretations of recent results in the theory of elliptic special functions (due to, among many others, Frenkel, Turaev, Spiridonov, and Zhedanov in the…
Superconformal indices, dualities and integrability
- Physics, Mathematics
- 2016
In this thesis we discuss exact, non-perturbative results achieved using superconformal index technique in supersymmetric gauge theories with four supercharges (which is N = 1 supersymmetry in four…
Mathematical structures behind supersymmetric dualities
- Mathematics
- 2015
The purpose of these notes is to give a short survey of an interesting connection between partition functions of supersymmetric gauge theories and hypergeometric functions and to present the recent…
More basic hypergeometric limits of the elliptic hypergeometric beta integral
- Mathematics
- 2013
In this article we continue the work from arXiv:0902.0621. In that article Eric Rains and the present author considered the limits of the elliptic beta integral as p->0 while the parameters t_r have…
References
SHOWING 1-10 OF 18 REFERENCES
Transformations of elliptic hypergeometric integrals
- Mathematics
- 2010
We prove a pair of transformations relating elliptic hypergeometric integrals of different dimensions, corresponding to the root systems BC_n and A_n; as a special case, we recover some integral…
Limits of multivariate elliptic hypergeometric biorthogonal functions
- Mathematics
- 2011
In this article we extend the results of our article "Limits of elliptic hypergeometric biorthogonal functions" to the multivariate setting. In that article we determined which families of…
Theta hypergeometric integrals
- Mathematics
- 2003
We define a general class of (multiple) integrals of hypergeometric type associated with the Jacobi theta functions. These integrals are related to theta hypergeometric series through the residue…
On BC type basic hypergeometric orthogonal polynomials
- Mathematics
- 1997
The five parameter family of multivariable Askey-Wilson polynomials is studied with four parameters generically complex. The multivariable Askey-Wilson polynomials form an orthogonal system with…
Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions
- Mathematics
- 2009
We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic…
BCn-symmetric polynomials
- Mathematics
- 2005
AbstractWe consider two important families of BCn-symmetric polynomials, namely Okounkov's
interpolation polynomials and Koornwinder's orthogonal
polynomials. We give a family of difference equations…
First order analytic difference equations and integrable quantum systems
- Mathematics
- 1997
We present a new solution method for a class of first order analytic difference equations. The method yields explicit “minimal” solutions that are essentially unique. Special difference equations…
$BC_n$-symmetric abelian functions
- Mathematics
- 2004
We construct a family of BC_n-symmetric biorthogonal abelian functions generalizing
Koornwinder's orthogonal polynomials, and prove a number of their properties, most notably
analogues of…
Multivariable q-Racah polynomials
- Mathematics
- 1996
The Koornwinder-Macdonald multivariable generalization of the Askey-Wilson polynomials is studied for parameters satisfying a truncation condition such that the orthogonality measure becomes discrete…
Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions
- Mathematics
- 1997
Various results in algebra, analysis, and geometry can be generalized by replacing the ordinary numbers (integer, real or complex) by their trigonometric analogues. For x ∈ ℂ, the trigonometric…