Towards the Convergence of Generalized Power Series Solutions of Algebraic ODEs

DOI10.1007/978-3-319-52842-7_7zbMath1404.34102OpenAlexW2713901219MaRDI QIDQ4644997

Irina Goryuchkina, Renat Gontsov

Publication date: 9 January 2019

Published in: Trends in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-52842-7_7

zbMATH Keywords

convergenceformal solutiongeneralized power seriesalgebraic ODE

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25)

Cites Work

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• Power expansions of solutions to the modified third Painlevé equation in a neighborhood of zero
• A family of solutions of a nonlinear ordinary differential equation and its application to Painlevé equations (III), (V) and (VI)
• Pole distribution of PVI transcendents close to a critical point
• A review of the sixth Painlevé equation
• Asymptotic expansions of solutions of the sixth Painlevé equation
• On the convergence of generalized power series satisfying an algebraic ODE
• Asymptotic behaviour and expansions of solutions of an ordinary differential equation
• Asymptotic expansions of solutions to the fifth Painlevé equation in neighbourhoods of singular and nonsingular points of the equation

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