On the Umemura Polynomials for the Painlev\'e III equation
classification
solv-int
nlin.SI
keywords
determinantequationexpressionpainlevpolynomialsrationalsolutionsapplying
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A determinant expression for the rational solutions of the Painlev\'e III (P$_{\rm III}$) equation whose entries are the Laguerre polynomials is given. Degeneration of this determinant expression to that for the rational solutions of P$_{\rm II}$ is discussed by applying the coalescence procedure.
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