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

2013/10/20 by Anastasia Parusnikova, Parusnikova, Anastasia
Mathematics · #34m25 #34m55 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:34m25 #msc:34m55

paper · pdf · doi:10.48550/arxiv.1310.5345

9 pages, 1 figure

arxiv created 2013/10/20 · arxiv updated 2013/10/22

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.

Related

• Power and non-power expansions of the solutions for the fourth-order analogue to the second Painlevé equation
• Power solution expansions of the analogue tothe first Painleve equation
• On Divergence of Puiseux Series Asymptotic Expansions of Solutions to the Third Painlevé Equation
• The Painlevé transcendents with solvable monodromy
• Algebraic relations between solutions of Painlevé equations