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

Abstract

We consider the Hankel determinant representation for the rational solutions of the Painlevé II equation. We give an explicit formula for the generating function of the entries in terms of logarithmic derivative of the Airy function, which by itself is a particular solution of the Painlevé II equation.

7 pages

References in corpus (2)

• Determinant Structure of the Rational Solutions for the Painlevé II Equation
• Determinant Formulas for the Toda and Discrete Toda Equations

Cited by in corpus (9)

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• Rational Solutions of the Painlevé-II Equation Revisited
• On symmetries of the non-stationary PIIn hierarchy and their applications
• Generating Function Associated with the Hankel Determinant Formula for the Solutions of the Painlevé IV Equation
• Determinant structure for tau-function of holonomic deformation of linear differential equations
• Toda-Schrödinger correspondence and orthogonal polynomials
• Almost Product Evaluation of Hankel Determinants