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

@article{Suzuki2010APS,
title={A Particular Solution of a Painlev{\'e} System in Terms of the Hypergeometric Function n+1 F n},
author={Takao Suzuki},
journal={Symmetry Integrability and Geometry-methods and Applications},
year={2010},
volume={6},
pages={078}
}
• Takao Suzuki
• Published 1 April 2010
• Mathematics
• Symmetry Integrability and Geometry-methods and Applications
In a recent work, we proposed the coupled Painleve VI system with A (1)n+1 - symmetry, which is a higher order generalization of the sixth Painleve 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 Painleve system derived from the confluence of n+1Fn.
In our previous work, a unified description as polynomial Hamiltonian systems was established for a broad class of the Schlesinger systems including the sixth Painleve equation and Garnier systems.
In this article we introduce a higher order generalization of the $q$-Painlev\'e VI equation given by Jimbo and Sakai. It is expressed as a system of $q$-difference evolution equations of $2n$-th
In this article, we propose a q-analogue of the Drinfeld-Sokolov hierarchy of type A. We also discuss its relationship with the q-Painleve VI equation and the q-hypergeometric function.
In this article, we propose a class of six-dimensional Painleve systems given as the monodromy preserving deformations of the Fuchsian systems. They are expressed as polynomial Hamiltonian systems of
In this article we propose an extension of Appell hypergeometric function $F_2$ (or equivalently $F_3$). It is derived from a particular solution of a higher order Painlev\'e system in two variables.
A relationship between Painleve systems and infinite-dimensional integrable hierarchies is studied. We derive a class of higher order Painleve systems from Drinfeld-Sokolov (DS) hierarchies of type A
This is the last part of a series of three papers entitled "Four-dimensional Painlev\'e-type equations associated with ramified linear equations". In this series of papers we aim to construct the
• Mathematics
Symmetry, Integrability and Geometry: Methods and Applications
• 2018
We derive Fredholm determinant and series representation of the tau function of the Fuji-Suzuki-Tsuda system and its multivariate extension, thereby generalizing to higher rank the results obtained
• Mathematics
• 2012
Recently, higher order generalizations of P_{\mathrm{V}\mathrm{I}} has been studied from two viewpoints, similarity reductions of infinite dimensional integrable hierarchies and monodromy preserving
• Mathematics, Physics
• 2012
Four 4-dimensional Painleve-type equations are obtained by isomonodromic deformation of Fuchsian equations: they are the Garnier system in two variables, the Fuji-Suzuki system, the Sasano system,

## References

SHOWING 1-5 OF 5 REFERENCES

A relationship between Painleve systems and infinite-dimensional integrable hierarchies is studied. We derive a class of higher order Painleve systems from Drinfeld-Sokolov (DS) hierarchies of type A
• Mathematics
• 1988
On etudie l'equation hypergeometrique generalisee en la reduisant a un systeme de la forme: (tI-B)dx/dt=Ax, ou t∈C, x un vecteur colonne complexe, A et B sont des matrices carrees constantes
The UC hierarchy is an extension of the KP hierarchy, which possesses not only an infinite set of positive time evolutions but also that of negative ones. Through a similarity reduction we derive
1. Elements of Differential Equations.- 1.1 Cauchy's existence theorem.- 1.2 Linear equations.- 1.3 Local behavior around regular singularities (Frobenius's method).- 1.4 Fuchsian equations.- 1.5
• Mathematics
• 2009
We study the Drinfeld-Sokolov hierarchies of type A_n^{(1)} associated with the regular conjugacy classes of W(A_n). A class of fourth order Painleve systems is derived from them by similarity