Generating Function Associated with the Determinant Formula for the Solutions of the Painleve' II Equation
Exactly Solvable and Integrable Systems
2007-05-23 v2 Mathematical Physics
math.MP
Abstract
In this paper we consider a Hankel determinant formula for generic solutions of the Painleve' II equation. We show that the generating functions for the entries of the Hankel determinants are related to the asymptotic solution at infinity of the linear problem of which the Painleve' II equation describes the isomonodromic deformations.
Keywords
Cite
@article{arxiv.nlin/0406035,
title = {Generating Function Associated with the Determinant Formula for the Solutions of the Painleve' II Equation},
author = {Nalini Joshi and Kenji Kajiwara and Marta Mazzocco},
journal= {arXiv preprint arXiv:nlin/0406035},
year = {2007}
}
Comments
9 pages, dedicated to Jean Pierre Ramis. A comment on summability is added