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

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.

9 pages, dedicated to Jean Pierre Ramis. A comment on summability is added

References in corpus (1)

• Generating Function Associated with the Rational Solutions of the Painlevé II Equation

Cited by in corpus (4)

• The recurrence coefficients of semi-classical Laguerre polynomials and the fourth Painlevé equation
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• Generating Function Associated with the Hankel Determinant Formula for the Solutions of the Painlevé IV Equation
• Toda-Schrödinger correspondence and orthogonal polynomials