Geodesic
Power-elliptic expansions of solutions to an ordinary differential equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 12, pp. 2206-2218 
A. D. Bruno. Power-elliptic expansions of solutions to an ordinary differential equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 12, pp. 2206-2218. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_12_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A rather general ordinary differential equation is considered that can be represented as a polynomial in variables and derivatives. For this equation, the concept of power-elliptic expansions of its solutions is introduced and a method for computing them is described. It is shown that such expansions of solutions exist for the first and second Painlevé equations.

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