Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 078, 11 pages      arXiv:1004.0059
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+1Fn

Takao Suzuki
Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan

Received June 23, 2010, in final form September 29, 2010; Published online October 07, 2010

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.

Key words: affine Weyl group; generalized hypergeometric functions; Painlevé equations.

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