On Divergence of Puiseux Series Asymptotic Expansions of Solutions to the Third Painlevé Equation

2017/02/19 by Parusnikova, Anastasia, Vasilyev, Andrey
#34M25 #34M55 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1702.05758

Abstract

In this paper we present a family of values of the parameters of the third Painlevé equation such that Puiseux series formally satisfying this equation -- considered as series of z^2/3 -- are series of exact Gevrey order one. We prove the divergence of these series and provide analytic functions which are approximated by them in sectors with the vertices at infinity.

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