We give a brief survey of the theory of elliptic hypergeometric functions - a new class of special functions discovered around ten years ago. Main topics to be discussed: the elliptic gamma function and elliptic beta integral, generalizing Euler's gamma function and beta integral; an elliptic analogue of the Gauss hypergeometric function; an elliptic extension of the Selberg integral; elliptic biorthogonal functions, generalizing classical orthogonal polynomials.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/158