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

Abstract

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.