On the Umemura Polynomials for the Painlev\'e III equation
solv-int
2009-10-31 v1 Exactly Solvable and Integrable Systems
Abstract
A determinant expression for the rational solutions of the Painlev\'e III (P) equation whose entries are the Laguerre polynomials is given. Degeneration of this determinant expression to that for the rational solutions of P is discussed by applying the coalescence procedure.
Keywords
Cite
@article{arxiv.solv-int/9903015,
title = {On the Umemura Polynomials for the Painlev\'e III equation},
author = {K. Kajiwara and T. Masuda},
journal= {arXiv preprint arXiv:solv-int/9903015},
year = {2009}
}
Comments
10 pages, LaTeX 2.09(Elsevier style), submitted to Phys. Lett. A