Year: 2008
Type: article
Abstract: We give a brief review of the main results of the theory of elliptic hypergeometric functions -- a new class of special functions of mathematical physics. We prove the most general univariate exact integration formula generalizing Euler's beta integral, which 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 particular subcases are described. We list known elliptic beta integrals on root systems and consider symmetry transformations for the corresponding elliptic hypergeometric functions of the higher order.
Source: Russian Mathematical Surveys
Author: V P Spiridonov
Institutions: Max Planck Society, Max Planck Institute for Mathematics
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1968073185