Symbolic integration of meromorphic differential systems via Dirichlet functions Original Research Article

We present a symbolic technique for computing the exact or approximate solutions of linear differential systems with meromorphic coefficients. To any system of that form, we attach a non-commutative generating series F. The combinatorial decomposition of F allows to get the solution as a polynomial in Dirichlet functions, or hypergeometric functions, that are built from the coefficients of the system.