On the convergence of formal exotic series solutions of an ODE

DOI10.1007/s40315-020-00306-zzbMath1448.34159OpenAlexW3004166659MaRDI QIDQ2188302

Renat Gontsov, Irina Goryuchkina

Publication date: 10 June 2020

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40315-020-00306-z

zbMATH Keywords

formal solutionconvergent seriesanalytic ODEimplicit mapping theorem

Mathematics Subject Classification ID

Applications of operator theory to differential and integral equations (47N20) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25) Nonlinear ordinary differential equations and systems in the complex domain (34M04)

Cites Work

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• Local expansions of solutions to the fifth Painlevé equation
• Exotic expansions of solutions to an ordinary differential equation
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• A \(\tau \)-function solution of the sixth Painlevé transcendent
• On the convergence of generalized power series satisfying an algebraic ODE
• Tabulation of Painlevé 6 transcendents
• Convergence of formal Dulac series satisfying an algebraic ordinary differential equation
• CRITICAL BEHAVIOURS OF THE FIFTH PAINLEVÉ TRANSCENDENTS AND THE MONODROMY DATA

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