zbMATH — the first resource for mathematics

Formal solutions of linear meromorphic differential systems and summability. (Solutions formelles des systèmes différentiels linéaires méromorphes et sommation.) (French) Zbl 0831.34002
This paper is an introductory text on the formal solutions of complex linear ordinary differential equations with meromorphic coefficients and on methods for getting actual analytic solutions from the formal ones. In the first part, a complete set of formal solutions is given with some ideas on algorithms for computing them based on Newton polygons and the Frobenius method. The second part deals with the summation of divergent series. Finally, the author proves the summability of formal solutions in two significant cases.

34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain
34A30 Linear ordinary differential equations and systems
34E05 Asymptotic expansions of solutions to ordinary differential equations
40G99 Special methods of summability