VP Spiridonov, “On the elliptic beta function”, Uspekhi Mat. Nauk, 56:1(337) (2001), 181–182;
Russian Math. Surveys, 56:1 (2001), 185–186 Russian Mathematical Surveys RUS ENG …

This is a brief survey of the main results of the theory of elliptic hypergeometric functions--a
new class of special functions of mathematical physics. A proof is given of the most general …

This updated edition will continue to meet the needs for an authoritative comprehensive
analysis of the rapidly growing field of basic hypergeometric series, or q-series. It includes …

We prove a pair of transformations relating elliptic hypergeometric integrals of different
dimensions, corresponding to the root systems BC n and A n; as a special case, we recover …

In this chapter we introduce the basic concepts of this thesis and give an impression of some
of the methods used to study them. Moreover we describe the connections to other parts of …

The univariate elliptic beta integral was discovered by the author in 2000. Recently
Bazhanov and Sergeev have interpreted it as a star-triangle relation (STR). This important …

We define a general class of (multiple) integrals of hypergeometric type associated with the
Jacobi theta functions. These integrals are related to theta hypergeometric series through …

We construct a family of BC n-symmetric biorthogonal abelian functions generalizing
Koornwinder's orthogonal polynomials (see [10]) and prove a number of their properties …

A general class of (multiple) hypergeometric type integrals associated with the Jacobi theta
functions is defined. These integrals are related to theta hypergeometric series via the …

We introduce elliptic weights of boxed plane partitions and prove that they give rise to a
generalization of MacMahon's product formula for the number of plane partitions in a box …