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ISSN: 2333-9721
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A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function {}_{n+1}F_n

Keywords: affine Weyl group , generalized hypergeometric functions , Painlevé equations

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Abstract:

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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