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Generating Function Associated with the Determinant Formula for the Solutions of the Painleve' II Equation

Nalini Joshi·Kenji Kajiwara·Marta Mazzocco
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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.

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Nalini Joshi, Kenji Kajiwara, Marta Mazzocco. 2004-09-08. Generating Function Associated with the Determinant Formula for the Solutions of the Painleve' II Equation. https://arxiv.org/abs/nlin/0406035

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