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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 074, 21 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.074
(Mi sigma1611)
 

This article is cited in 7 scientific papers (total in 7 papers)

The Endless Beta Integrals

Gor A. Sarkissianabc, Vyacheslav P. Spiridonovba

a Laboratory of Theoretical Physics, JINR, Dubna, 141980, Russia
b St. Petersburg Department of the Steklov Mathematical Institute of Russian Academy of Sciences, Fontanka 27, St. Petersburg, 191023 Russia
c Department of Physics, Yerevan State University, Yerevan, Armenia
Full-text PDF (480 kB) Citations (7)
References:
Abstract: We consider a special degeneration limit $\omega_1\to - \omega_2$ (or $b\to {\rm i}$ 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 $\mathrm{SL}(2,\mathbb{C})$ group. A new similar nontrivial hypergeometric degeneration of the Faddeev modular quantum dilogarithm (or hyperbolic gamma function) is discovered in the limit $\omega_1\to \omega_2$ (or $b\to 1$).
Keywords: elliptic hypergeometric functions, complex gamma function, beta integrals, star-triangle relation.
Funding agency Grant number
Russian Science Foundation 19-11-00131
The key results of this work were obtained within the research program of project no. 19-11-00131 supported by the Russian Science Foundation.
Received: May 5, 2020; in final form July 24, 2020; Published online August 5, 2020
Bibliographic databases:
Document Type: Article
MSC: 33D60, 33E20
Language: English
Citation: Gor A. Sarkissian, Vyacheslav P. Spiridonov, “The Endless Beta Integrals”, SIGMA, 16 (2020), 074, 21 pp.
Citation in format AMSBIB
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\by Gor~A.~Sarkissian, Vyacheslav~P.~Spiridonov
\paper The Endless Beta Integrals
\jour SIGMA
\yr 2020
\vol 16
\papernumber 074
\totalpages 21
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  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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    References:22
     
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