A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function n+1Fn
In a recent work, we proposed the coupled Painlevé VI system with A2n+1⁽¹⁾-symmetry, which is a higher order generalization of the sixth Painlevé equation (PVI). In this article, we present its particular solution expressed in terms of the hypergeometric function n+1Fn. We also discuss a degeneratio...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2010 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2010
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146500 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function n+1Fn / T. Suzuki // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 6 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862746944387940352 |
|---|---|
| author | Suzuki, T. |
| author_facet | Suzuki, T. |
| citation_txt | A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function n+1Fn / T. Suzuki // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In a recent work, we proposed the coupled Painlevé VI system with A2n+1⁽¹⁾-symmetry, which is a higher order generalization of the sixth Painlevé equation (PVI). In this article, we present its particular solution expressed in terms of the hypergeometric function n+1Fn. We also discuss a degeneration structure of the Painlevé system derived from the confluence of n+1Fn.
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| first_indexed | 2025-12-07T20:48:53Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146500 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:48:53Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Suzuki, T. 2019-02-09T19:27:04Z 2019-02-09T19:27:04Z 2010 A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function n+1Fn / T. Suzuki // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 6 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B80; 33C20; 34M55 DOI:10.3842/SIGMA.2010.078 https://nasplib.isofts.kiev.ua/handle/123456789/146500 In a recent work, we proposed the coupled Painlevé VI system with A2n+1⁽¹⁾-symmetry, which is a higher order generalization of the sixth Painlevé equation (PVI). In this article, we present its particular solution expressed in terms of the hypergeometric function n+1Fn. We also discuss a degeneration structure of the Painlevé system derived from the confluence of n+1Fn. This paper is a contribution to the Special Issue “Relationship of Orthogonal Polynomials and Special Functions with Quantum Groups and Integrable Systems”. The full collection is available at http://www.emis.de/journals/SIGMA/OPSF.html.
 The author would like to express his gratitude to Mr. Masaomi Miyamoto of Kobe University for fruitful discussion. The author is also grateful to Professors Masatoshi Noumi, Hidetaka Sakai, Teruhisa Tsuda and Yasuhiko Yamada for helpful comments and advices. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function n+1Fn Article published earlier |
| spellingShingle | A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function n+1Fn Suzuki, T. |
| title | A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function n+1Fn |
| title_full | A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function n+1Fn |
| title_fullStr | A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function n+1Fn |
| title_full_unstemmed | A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function n+1Fn |
| title_short | A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function n+1Fn |
| title_sort | particular solution of a painlevé system in terms of the hypergeometric function n+1fn |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146500 |
| work_keys_str_mv | AT suzukit aparticularsolutionofapainlevesystemintermsofthehypergeometricfunctionn1fn AT suzukit particularsolutionofapainlevesystemintermsofthehypergeometricfunctionn1fn |