On the Umemura Polynomials for the Painlevé III equation

Details On the Umemura Polynomials for the Painlevé III equation On the Umemura Polynomials for the Painlevé III equation

1999-03-24

arxiv.org/abs/solv-int/9903015v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages, LaTeX 2.09(Elsevier style), submitted to Phys. Lett. A

Scientific paper

10.1016/S0375-9601(99)00577-0

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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