Formal solutions and factorization of differential operators with power series coefficients

Abstract

The topic of this paper is formal solutions of linear differential equations with formal power series coefficients. The method proposed for computing these solutions is based on factorization of differential operators. The notion of exponential parts is introduced to give a description of factorization properties and to characterize the formal solutions. The algorithms will be described and their implementation is available. © 1997 Academic Press Limited.