In this paper we are concerned with rational solutions and associated polynomials for the second, third and fourth Painlevé equations. These rational solutions are expressible as in terms of special polynomials. The structure of the roots of these polynomials is studied and it is shown that these have a highly regular structure. © 2005 Springer Science+Business Media, Inc.
CITATION STYLE
Clarkson, P. A. (2005). Painlevé equations and associated polynomials. Developments in Mathematics, 13, 123–163. https://doi.org/10.1007/0-387-24233-3_7
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