Work

The Endless Beta Integrals

Year: 2020

Type: article

Abstract: We consider a special degeneration limit ω 1 → -ω 2 (or b → i in the context of 2d Liouville quantum field theory) for the most general univariate hyperbolic beta integral.This limit is also applied to the most general hyperbolic analogue of the Euler-Gauss hypergeometric function and its W (E 7 ) group of symmetry transformations.Resulting functions are identified as hypergeometric functions over the field of complex numbers related to the SL(2, C) group.A new similar nontrivial hypergeometric degeneration of the Faddeev modular quantum dilogarithm (or hyperbolic gamma function) is discovered in the limit ω 1 → ω 2 (or b → 1).

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2020.074

Authors: JINR, Russia, Gor A. Sarkissian, Vyacheslav P. Spiridonov, JINR, Russia

Institutions: Russian Academy of Sciences, Yerevan State University, St. Petersburg Department of Steklov Institute of Mathematics, Steklov Mathematical Institute, Joint Institute for Nuclear Research

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Russian Science Foundation

Award: G6054974904