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KIAM Preprint № 65, Moscow, 2013
Authors: Goryuchkina I. V.
On convergence of power series solution with nonrational power exponents of algebraic ODE
Abstract:
Here we prove the theorem on sufficient condition of the convergence near zero of the formal power series (with complex but nonrational power exponents) that satisfies to algebraic (polynomial) ordinary differential equation (ODE). The proof is based on classical majorant method, but for constructing majorant series we use methods of power geometry.
Keywords:
Convergence, algebraic ODEs, formal solutions, analytic functions
Publication language: russian,  pages: 24
Research direction:
Mathematical problems and theory of numerical methods
Russian source text:
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