%0 Journal Article
%T An analytic proof of the Malgrange-Sibuya theorem on the convergence of formal solutions of an ODE
%A R. R. Gontsov
%A I. V. Goryuchkina
%J Mathematics
%D 2013
%I arXiv
%X We propose an analytic proof of the Malgrange-Sibuya theorem concerning a sufficient condition of the convergence of a formal power series satisfying an ordinary differential equation. The proof is based on the majorant method and allows to estimate the radius of convergence of such a series.
%U http://arxiv.org/abs/1311.6416v1