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arXiv · 1702.05758

On Divergence of Puiseux Series Asymptotic Expansions of Solutions to the Third Painlev\'{e} Equation

Anastasia Parusnikova·Andrey Vasilyev
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Abstract

In this paper we present a family of values of the parameters of the third Painlev\'{e} 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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BibTeXRIS

Anastasia Parusnikova, Andrey Vasilyev. 2017-02-19. On Divergence of Puiseux Series Asymptotic Expansions of Solutions to the Third Painlev\'{e} Equation. https://arxiv.org/abs/1702.05758

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