A Parallel Algorithm for the Hadamard Product of Holonomic Formal Series

In this work we consider the class of the holonomic formal series and we study how, given two linear differential equations with polynomial coefficients verified by two holonomic series Φ1 and Φ2, it is possible to compute a linear differential equation satisfied by the Hadamard product of Φ1 and Φ2. We give a parallel algorithm for this problem and we show that it belongs to NC2.