
SIGMA 6 (2010), 078, 11 pages arXiv:1004.0059
http://dx.doi.org/10.3842/SIGMA.2010.078
Contribution to the Special Issue “Relationship of Orthogonal Polynomials and Special Functions with Quantum Groups and Integrable Systems”
A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function _{n+1}F_{n}
Takao Suzuki
Department of Mathematics, Kobe University, Rokko, Kobe 6578501, Japan
Received June 23, 2010, in final form September 29, 2010; Published online October 07, 2010
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}.
Key words:
affine Weyl group; generalized hypergeometric functions; Painlevé equations.
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