On the elliptic beta function (Q2784537)

Recently, \textit{V. Spiridonov} and \textit{A. Zhedanov} [Commun. Math. Phys. 210, No. 1, 49--83 (2000; Zbl 0989.30008)] considered a finite-dimensional class of some biorthogonal rational functions with a discrete measure. Here, in the paper under review, the author proves an elliptic generalization of the familiar basis (or \(q\)-) beta integral which is equivalent to a normalization condition on a continuous weight function of such biorthogonal rational functions, expressed in terms of basic (or \(q\)-) hypergeometric series. The main results are presented as Theorem 1 and Theorem 2, which are much too involved to be reproduced in this review.