Formal Solutions of Linear Differential Systems with Essential Singularities in their Coefficients

International audienceThe local analysis of formal meromorphic linear differential systems with coefficients in C((z)) has been widely studied in the literature and there exist various computer algebra algorithms for computing formal solutions of such systems. In the present paper we extend the algorithm presented in [3] to allow more general systems. More precisely, we give an algorithm for computing a formal fundamental matrix of solutions around z=0 of systems with coefficients in C((z))[[X]], where X is transcendental and hyperexponential over C((z))