Hypergeometric solution of a certain polynomial Hamiltonian system of isomonodromy type

Details Hypergeometric solution of a certain polynomial Hamiltonian system of isomonodromy type Hypergeometric solution of a certain polynomial Hamiltonian system of isomonodromy type

2010-05-22

arxiv.org/abs/1005.4130v4

Mathematics

Classical Analysis and ODEs

16 pages, no figure

Scientific paper

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. The main purpose of this paper is to present particular solutions of this Hamiltonian system in terms of a certain generalization of Gauss' hypergeometric function. Key ingredients of the argument are the linear Pfaffian system derived from an integral representation of the hypergeometric function (with the aid of twisted de Rham theory) and Lax formalism of the Hamiltonian system.

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