Corpus ID: 119124997

Aspects of elliptic hypergeometric functions

@article{Spiridonov2013AspectsOE,
  title={Aspects of elliptic hypergeometric functions},
  author={Vyacheslav Pavlovich Spiridonov},
  journal={arXiv: Classical Analysis and ODEs},
  year={2013}
}
  • V. Spiridonov
  • Published 10 July 2013
  • Mathematics, Physics
  • arXiv: Classical Analysis and ODEs
General elliptic hypergeometric functions are defined by elliptic hypergeometric integrals. They comprise the elliptic beta integral, elliptic analogues of the Euler-Gauss hypergeometric function and Selberg integral, as well as elliptic extensions of many other plain hypergeometric and $q$-hypergeometric constructions. In particular, the Bailey chain technique, used for proving Rogers-Ramanujan type identities, has been generalized to integrals. At the elliptic level it yields a solution of… Expand
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References

SHOWING 1-10 OF 61 REFERENCES
Limits of elliptic hypergeometric integrals
Abstract In Ann. Math., to appear, 2008, the author proved a number of multivariate elliptic hypergeometric integrals. The purpose of the present note is to explore more carefully the variousExpand
Theta hypergeometric integrals
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 residueExpand
Transformations of elliptic hypergeometric integrals
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 integralExpand
An elliptic hypergeometric beta integral transformation
In this article we prove a new elliptic hypergeometric integral identity. It previously appeared (as a conjecture) in articles by Rains, and Spiridonov and Vartanov. Moreover it gives a differentExpand
An elliptic hypergeometric integral with W(F4) symmetry
In this article we give a new transformation between elliptic hypergeometric beta integrals, which gives rise to a Weyl group symmetry of type F4. The transformation is a generalization of a seriesExpand
Properties of Generalized Univariate Hypergeometric Functions
Based on Spiridonov’s analysis of elliptic generalizations of the Gauss hypergeometric function, we develop a common framework for 7-parameter families of generalized elliptic, hyperbolic andExpand
Continuous biorthogonality of the elliptic hypergeometric function
We construct a family of continuous biorthogonal functions related to an elliptic analogue of the Gauss hypergeometric function. The key tools used for that are the elliptic beta integral and theExpand
Yang-Baxter equation, parameter permutations, and the elliptic beta integral
This paper presents a construction of an infinite-dimensional solution of the Yang-Baxter equation of rank?1 which is represented as an integral operator with an elliptic hypergeometric kernel actingExpand
The Elliptic Gamma Function and SL(3, Z)⋉Z3
Abstract The elliptic gamma function is a generalization of the Euler gamma function and is associated to an elliptic curve. Its trigonometric and rational degenerations are the Jackson q-gammaExpand
Inversions of integral operators and elliptic beta integrals on root systems
We prove a novel type of inversion formula for elliptic hypergeometric integrals associated to a pair of root systems. Using the (A,C) inversion formula to invert one of the known C-type ellipticExpand
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