Multisummability of formal power series solutions of linear ordinary differential equations

Article type: Research Article

Authors: Balser, W. | Braaksma, B.L.J. | Ramis, J.-P. | Sibuya, Y.

Affiliations: Universität Ulm, Abteilung Mathematik V, Oberer Eselsberg, D-7900 Ulm/Donau, Germany | Mathematisch Instituut, Rijksuniversiteit Groningen, Postbus 800, 9700 AV Groningen, Netherlands | Département de Mathématiques, Université de Strasbourg, 7, rue René Descartes, 67084 Strasbourg, France | School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA

Abstract: If f is a formal power series solution of a linear meromorphic differential equation, then it is shown that f=f1+…+fq, were fj is hj-summable; here h1,…hq are slopes of the associated Newton polygon. The multisummability properties of fundamental solutions of linear homogeneous meromorphic differential equations are studied.

DOI: 10.3233/ASY-1991-5102

Journal: Asymptotic Analysis, vol. 5, no. 1, pp. 27-45, 1991