Essays on the theory of elliptic hypergeometric functions

@article{Spiridonov2008EssaysOT,
  title={Essays on the theory of elliptic hypergeometric functions},
  author={V P Spiridonov},
  journal={Russian Mathematical Surveys},
  year={2008},
  volume={63},
  pages={405-472}
}
  • V. Spiridonov
  • Published 20 May 2008
  • Mathematics
  • Russian Mathematical Surveys
This is a brief survey of the main results of the theory of elliptic hypergeometric functions -- a new class of special functions of mathematical physics. A proof is given of the most general known univariate exact integration formula generalizing Euler's beta integral. It is called the elliptic beta integral. An elliptic analogue of the Gauss hypergeometric function is constructed together with the elliptic hypergeometric equation for it. Biorthogonality relations for this function and its… 
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136 Citations
Highly Influential Citations
5
Background Citations
56
Methods Citations
14
Results Citations
1

136 Citations

Introduction to the Theory of Elliptic Hypergeometric Integrals

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  • V. Spiridonov
  • Mathematics
    Lectures on Orthogonal Polynomials and Special Functions
  • 2020
This is author's Habilitation Thesis (Dr. Sci. dissertation) submitted at the beginning of September 2004. It is written in Russian and is posted due to the continuing requests for the manuscript. …

Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions

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Elliptic Hypergeometric Laurent Biorthogonal Polynomials with a Dense Point Spectrum on the Unit Circle

Using the technique of the elliptic Frobenius determinant, we construct new elliptic solutions of theQD-algorithm. These solutions can be interpreted as elliptic solutions of the discrete-time Toda…

Elliptic Hypergeometry of Supersymmetric Dualities

We give a full list of known $${\mathcal{N}=1}$$ supersymmetric quantum field theories related by the Seiberg electric-magnetic duality conjectures for SU(N), SP(2N) and G2 gauge groups. Many of the…

A noncommutative weight-dependent generalization of the binomial theorem

A weight-dependent generalization of the binomial theorem for noncommuting variables is presented. This result extends the well-known binomial theorem for q-commuting variables by a generic weight…

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 acting…

New Elliptic Solutions of the Yang–Baxter Equation

We consider finite-dimensional reductions of an integral operator with the elliptic hypergeometric kernel describing the most general known solution of the Yang–Baxter equation with a rank 1 symmetry…
...

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