On Gevrey orders of power expansions of solutions to the third and fifth Painlevé equations

Abstract

The question under consideration is Gevrey summability of power expansions of solutions to the third and fifth Painlevé equations near infinity. Methods of French and Japaneese schools are used to analyse these properties of formal power-series solutions. The results obtained are compared with the ones obtained by means of Power Geometry.

arXiv comment9 pages, 1 figure