An analytic proof of the Malgrange-Sibuya theorem on the convergence of formal solutions of an ODE

Published 25 Nov 2013 in math.CA | (1311.6416v1)

Abstract: 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.

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