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On the Umemura Polynomials for the Painlevé III equation

K. Kajiwara·T. Masuda
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Abstract

A determinant expression for the rational solutions of the Painlevé 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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K. Kajiwara, T. Masuda. 1999-03-24. On the Umemura Polynomials for the Painlevé III equation. https://doi.org/10.1016/s0375-9601(99)00577-0

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