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Painlevé Equations and Associated Polynomials

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Theory and Applications of Special Functions

Part of the book series: Developments in Mathematics ((DEVM,volume 13))

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Abstract

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.

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Authors and Affiliations

  1. Institute of Mathematics, Statistics & Actuarial Science, University of Kent, Canterbury, CT2 7NF, UK

    Peter A. Clarkson

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  1. Peter A. Clarkson
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Editors and Affiliations

  1. University of Central Florida, USA

    Mourad E.H. Ismail

  2. Technische Universiteit Delft, The Netherlands

    Erik Koelink

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Clarkson, P.A. (2005). Painlevé Equations and Associated Polynomials. In: Ismail, M.E., Koelink, E. (eds) Theory and Applications of Special Functions. Developments in Mathematics, vol 13. Springer, Boston, MA. https://doi.org/10.1007/0-387-24233-3_7

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