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math.CA2017
On Divergence of Puiseux Series Asymptotic Expansions of Solutions to the Third Painlevé Equation
Anastasia Parusnikova, Andrey Vasilyev
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 $…
math.CA2014
4-Dimensional Power Geometry and its Application to --
Anastasia Parusnikova
In the first section of this work we introduce 4-dimensional Power Geometry for second-order ODEs of a polynomial form. In the next five sections we apply this construction to the…
math.CA2013
On Gevrey orders of power expansions of solutions to the third and fifth Painlevé equations
Anastasia Parusnikova
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 sch…