A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function {}_{n+1}F_n
In a recent work, we proposed the coupled Painlevé VI system with A_{2n+1}^{(1)}-symmetry, which is a higher order generalization of the sixth Painlevé equation (P_{VI}). In this article, we present its particular solution expressed in terms of the hypergeometric function {}_{n+1}F_n. We also discus...
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2010-10-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Online Access: | http://dx.doi.org/10.3842/SIGMA.2010.078 |
| Summary: | In a recent work, we proposed the coupled Painlevé VI system with A_{2n+1}^{(1)}-symmetry, which is a higher order generalization of the sixth Painlevé equation (P_{VI}). In this article, we present its particular solution expressed in terms of the hypergeometric function {}_{n+1}F_n. We also discuss a degeneration structure of the Painlevé system derived from the confluence of {}_{n+1}F_n. |
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| ISSN: | 1815-0659 |