255 citations · 1.5k across the 50 of their papers we have counts for
16 papers · 1 filter
Rational hypergeometric identities
Gor A. Sarkissian, Vyacheslav P. Spiridonov
A special singular limit is considered for the Faddeev modular quantum dilogarithm (hyperbolic gamma function) and the corresponding hyperbolic integrals. It brings…
Introduction to the theory of elliptic hypergeometric integrals
V. P. Spiridonov
We give a brief account of the key properties of elliptic hypergeometric integrals -- a relatively recently discovered top class of transcendental special functions of hypergeometr…
Matrix Bailey Lemma and the Star-Triangle Relation
Kamil Yu. Magadov, Vyacheslav P. Spiridonov
We compare previously found finite-dimensional matrix and integral operator realizations of the Bailey lemma employing univariate elliptic hypergeometric functions. With the help o…
Rarefied elliptic hypergeometric functions
V. P. Spiridonov
Two exact evaluation formulae for multiple rarefied elliptic beta integrals related to the simplest lens space are proved. They generalize evaluations of the type I and II elliptic…
Aspects of elliptic hypergeometric functions
V. P. Spiridonov
General elliptic hypergeometric functions are defined by elliptic hypergeometric integrals. They comprise the elliptic beta integral, elliptic analogues of the Euler-Gauss hypergeo…
Elliptic hypergeometric terms
V. P. Spiridonov
General structure of the multivariate plain and q-hypergeometric terms and univariate elliptic hypergeometric terms is described. Some explicit examples of the totally elliptic hyp…
Essays on the theory of elliptic hypergeometric functions
V. P. Spiridonov
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…
Determinants of elliptic hypergeometric integrals
E. M. Rains, V. P. Spiridonov
We start from an interpretation of the -symmetric "Type I" (elliptic Dixon) elliptic hypergeometric integral evaluation as a formula for a Casoratian of the elliptic hypergeo…
Classical elliptic hypergeometric functions and their applications
V. P. Spiridonov
General theory of elliptic hypergeometric series and integrals is outlined. Main attention is paid to the examples obeying properties of the "classical" special functions. In parti…
Inversions of integral operators and elliptic beta integrals on root systems
Vyacheslav P. Spiridonov, S. Ole Warnaar
We prove a novel type of inversion formula for elliptic hypergeometric integrals associated to a pair of root systems. Using the (A,C) inversion formula to invert one of the known…
Short proofs of the elliptic beta integrals
V. P. Spiridonov
We give elementary proofs of the univariate elliptic beta integral with bases and its multiparameter generalizations to integrals on the and root systems.…
A multiparameter summation formula for Riemann theta functions
V. P. Spiridonov
We generalize Warnaar's elliptic extension of a Macdonald multiparameter summation formula to Riemann surfaces of arbitrary genus.
A Bailey tree for integrals
V. P. Spiridonov
The notion of integral Bailey pairs is introduced. Using the single variable elliptic beta integral, we construct an infinite binary tree of identities for elliptic hypergeometric…
Unit circle elliptic beta integrals
J. F. van Diejen, V. P. Spiridonov
We present some elliptic beta integrals with a base parameter on the unit circle, together with their basic degenerations.
Theta hypergeometric series
V. P. Spiridonov
We formulate general principles of building hypergeometric type series from the Jacobi theta functions that generalize the plain and basic hypergeometric series. Single and multiva…
Theta hypergeometric integrals
V. P. Spiridonov
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 thro…