Uniform Multisummability and Convergence of a Power Series

MR2075291 Yasutaka SIBUYA Yasutaka SIBUYA Uniform Multisummability and Convergence of a Power Series Funkcialaj Ekvacioj. Serio Internacia 47 2004 119--127 http://fe.math.kobe-u.ac.jp/FE/FullPapers/47-1/47_119.pdf http://www.ams.org/mathscinet-getitem?mr=MR2075291 The purpose of this paper is to give a sufficient condition for convergence of a multisummable power series. Previously, similar results had been obtained for formal solutions of ordinary differential equations and also of a completely integrable Pfaffian system. In those cases, proof was based heavily on the form of equations. But, in relatively recent developement, it was shown that formal solutions of ordinary differential equations at an irregular singular point are generally multisummable. In this paper, proof of convergence is totally independent of any equations and based only on multisummability of power series. Power series, Asymptotic expansions, Multisummability, Ordinary differential equations, Pfaffian systems, Singularity. 34A25, 34M30, 35C10. 47-119 2004 Uniform Multisummability and Convergence of a Power Series Yasutaka SIBUYA Yasutaka SIBUYA 1 Balser, W. Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations Universitext, Springer 2000 MR1722871

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