Multisummability of formal power series solutions of linear ordinary differential equations

Abstract

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