A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function n +1 F n

[摘要] In a recent work, we proposed the coupled Painlevé VI system with A 2 n +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 .

[关键词] af fine Weyl group;generalized hypergeometric functions;Painlev´e equations