An Elliptic Beta Integral
In December 1999 the author has conjectured an elliptic generalization of the Nassrallah-Rahman $q$-beta integral. It is defined in terms of the Ruijsenaars' elliptic gamma functions and depends on five parameters $t_0,...,t_4$ and two bases $p$ and $q$. In this talk we shall report an evaluation of this elliptic beta integral for a particular set of values of the parameters $t_m$. A multivariate extension of the conjecture, which was worked our recently by J.F. van Diejen and the author, will be discussed as well.