Essays on the theory of elliptic hypergeometric functions

Understand

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.