English

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 (PIII_{\rm III}) equation whose entries are the Laguerre polynomials is given. Degeneration of this determinant expression to that for the rational solutions of PII_{\rm II} 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