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

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

2001-12-27

arxiv.org/abs/nlin/0112043v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

7 pages

Scientific paper

10.1088/0305-4470/35/16/101

We consider the Hankel determinant representation for the rational solutions
of the Painlev\'e 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 Painlev\'e II
equation.

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