On the Umemura Polynomials for the Painlevé III equation
arXiv:solv-int/9903015 · doi:10.1016/S0375-9601(99)00577-0
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.
10 pages, LaTeX 2.09(Elsevier style), submitted to Phys. Lett. A