# 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} }

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…

## 136 Citations

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We start from an interpretation of the BC2-symmetric “Type I” (elliptic Dixon) elliptic hypergeometric integral evaluation as a formula for a Casoratian of the elliptic hypergeometric equation and…

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Abstract
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