# Essays on the theory of elliptic hypergeometric functions

@article{Spiridonov2008EssaysOT, title={Essays on the theory of elliptic hypergeometric functions}, author={Vyacheslav P. Spiridonov}, journal={Russian Mathematical Surveys}, year={2008}, volume={63}, pages={405-472} }

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…

## 155 Citations

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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 various…

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We consider an elliptic analogue of the Gauss hypergeometric function and two of its multivariate generalizations. We describe their relation to elliptic beta integrals, the exceptional Weyl group…

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