Geodesic
Special polynomials and rational solutions of the hierarchy of the second Painlevé equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 1, pp. 58-67

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We study special polynomials used to represent rational solutions of the hierarchy of the second Painlevé equation. We find several recursion relations satisfied by these polynomials. In particular, we obtain a differential–difference relation that allows finding any polynomial recursively. This relation is an analogue of the Toda chain equations.
Mots-clés : Painlevé equations, rational solution
Keywords: hierarchy of the second Painlevé equation, special polynomial, Toda chain. 
M. V. Demina; N. A. Kudryashov. Special polynomials and rational solutions of the hierarchy of the second Painlevé equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 1, pp. 58-67. http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a4/
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