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

Katsunori Iwasaki·Kenji Kajiwara·Toshiya Nakamura
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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.

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Katsunori Iwasaki, Kenji Kajiwara, Toshiya Nakamura. 2001-12-27. Generating Function Associated with the Rational Solutions of the Painlevé II Equation. https://doi.org/10.1088/0305-4470%2F35%2F16%2F101

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