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Working paper

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

math. arxive. Cornell University, 2017. No. 1702.05758.
Parusnikova A., Vasilyev A. V.
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.