Generating Function Associated with the Rational Solutions of the Painlev\'e II Equation
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🌊 nlin.SI
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equationfunctionpainlevgeneratingrationalsolutionsairyassociated
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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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