A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function ${}_{n+1}{F}_n$

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 ($P_{\mathrm{VI}}$). 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 ${}_{n+1}{F}_n$.

References in corpus (2)

• A class of higher order Painleve systems arising from integrable hierarchies of type A
• Drinfeld-Sokolov hierarchies of type A and fourth order Painleve systems

Cited by in corpus (9)

• Degeneration scheme of 4-dimensional Painlevé-type equations
• Four-Dimensional Painlevé-Type Equations Associated with Ramified Linear Equations III: Garnier Systems and Fuji-Suzuki Systems
• A class of higher order Painleve systems arising from integrable hierarchies of type A
• A q-analogue of the Drinfeld-Sokolov hierarchy of type A and q-Painleve system
• On solutions of the Fuji-Suzuki-Tsuda system
• Six-dimensional Painleve systems and their particular solutions in terms of hypergeometric functions
• A higher order Painlevé system in two variables and extensions of the Appell hypergeometric functions $F_1$, $F_2$ and $F_3$
• Integral formulas for quantum isomonodromic systems
• Hypergeometric solution of a certain polynomial Hamiltonian system of isomonodromy type