Apparent singularities of D-finite systems

摘要

We generalize the notions of singularities and ordinary points from linearordinary differential equations to D-finite systems. Ordinary points of aD-finite system are characterized in terms of its formal power seriessolutions. We also show that apparent singularities can be removed like in theunivariate case by adding suitable additional solutions to the system at hand.Several algorithms are presented for removing and detecting apparentsingularities. In addition, an algorithm is given for computing formal powerseries solutions of a D-finite system at apparent singularities.