The Endless Beta Integrals
We consider a special degeneration limit ω₁ → −ω₂ (or → i in the context of 2 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 (₇) group of...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210774 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The Endless Beta Integrals. Gor A. Sarkissian and Vyacheslav P. Spiridonov. SIGMA 16 (2020), 074, 21 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862686225170694144 |
|---|---|
| author | Sarkissian, Gor A. Spiridonov, Vyacheslav P. |
| author_facet | Sarkissian, Gor A. Spiridonov, Vyacheslav P. |
| citation_txt | The Endless Beta Integrals. Gor A. Sarkissian and Vyacheslav P. Spiridonov. SIGMA 16 (2020), 074, 21 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider a special degeneration limit ω₁ → −ω₂ (or → i in the context of 2 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 (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 ω₁ → ω₂ (or → 1).
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| first_indexed | 2026-03-17T12:52:51Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210774 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-17T12:52:51Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Sarkissian, Gor A. Spiridonov, Vyacheslav P. 2025-12-17T14:35:53Z 2020 The Endless Beta Integrals. Gor A. Sarkissian and Vyacheslav P. Spiridonov. SIGMA 16 (2020), 074, 21 pages 1815-0659 2020 Mathematics Subject Classification: 33D60; 33E20 arXiv:2005.01059 https://nasplib.isofts.kiev.ua/handle/123456789/210774 https://doi.org/10.3842/SIGMA.2020.074 We consider a special degeneration limit ω₁ → −ω₂ (or → i in the context of 2 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 (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 ω₁ → ω₂ (or → 1). This paper is based on the talk given by V.S. at the conference “Elliptic Integrable Systems, Special Functions and Quantum Field Theory”, June 16–20, 2019, Nordita, Stockholm. The key results of this work were obtained within the research program of project no. 19-11-00131 supported by the Russian Science Foundation. We thank T.H. Koornwinder and E.M. Rains for explanations on the uniformness of the limit for the q-gamma function (25) following from their works [22] and [29]. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Endless Beta Integrals Article published earlier |
| spellingShingle | The Endless Beta Integrals Sarkissian, Gor A. Spiridonov, Vyacheslav P. |
| title | The Endless Beta Integrals |
| title_full | The Endless Beta Integrals |
| title_fullStr | The Endless Beta Integrals |
| title_full_unstemmed | The Endless Beta Integrals |
| title_short | The Endless Beta Integrals |
| title_sort | endless beta integrals |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210774 |
| work_keys_str_mv | AT sarkissiangora theendlessbetaintegrals AT spiridonovvyacheslavp theendlessbetaintegrals AT sarkissiangora endlessbetaintegrals AT spiridonovvyacheslavp endlessbetaintegrals |