Generating function associated with the determinant formula for the solutions of the Painlevé II equation

Nalini Joshi; Kenji Kajiwara; Marta Mazzocco

Generating function associated with the determinant formula for the solutions of the Painlevé II equation

Nalini Joshi, Kenji Kajiwara, Marta Mazzocco

Division of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

In this paper we consider a Hankel determinant formula for generic solutions of the Painlevé 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 Painlevé II equation describes the isomonodromic deformations.

Original language	English
Pages (from-to)	67-78
Number of pages	12
Journal	Asterisque
Issue number	297
Publication status	Published - 2004

All Science Journal Classification (ASJC) codes

Mathematics(all)

Cite this

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title = "Generating function associated with the determinant formula for the solutions of the Painlev{\'e} II equation",

abstract = "In this paper we consider a Hankel determinant formula for generic solutions of the Painlev{\'e} 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 Painlev{\'e} II equation describes the isomonodromic deformations.",

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AU - Joshi, Nalini

AU - Kajiwara, Kenji

AU - Mazzocco, Marta

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AB - In this paper we consider a Hankel determinant formula for generic solutions of the Painlevé 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 Painlevé II equation describes the isomonodromic deformations.

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JO - Asterisque

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ER -

Generating function associated with the determinant formula for the solutions of the Painlevé II equation

Abstract

All Science Journal Classification (ASJC) codes

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