An Algorithm for Solving Linear Ordinary Differential Equations of Fuchsian Type with Three Singular Points

We propose a method for representing the solutions of a certain type of ordinary differential operator L in terms of those of more fundamental differential operators. This method consists of two steps, decomposing L in the ring of differential operators and then describing the projections to the components of this decomposition also in terms of some differential operators. We provide a concrete algorithm for the application of this method and show that this algorithm is successful for a specific example of a 6-th order homogeneous linear ordinary differential operator of Fuchsian type with three singular points.