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A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function n+1Fn
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function n+1Fn
Інший ID:
2010 Mathematics Subject Classification: 17B80; 33C20; 34M55
DOI:10.3842/SIGMA.2010.078
DOI:10.3842/SIGMA.2010.078
Посилання:
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.
Підтримка:
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.
Дата:
2010
Переглядів:
501
Завантажень:
231
Анотація:
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.
