Apparent Singularities of D-finite Systems
Symbolic Computation
2017-05-03 v1
Abstract
We generalize the notions of singularities and ordinary points from linear ordinary differential equations to D-finite systems. Ordinary points of a D-finite system are characterized in terms of its formal power series solutions. We also show that apparent singularities can be removed like in the univariate case by adding suitable additional solutions to the system at hand. Several algorithms are presented for removing and detecting apparent singularities. In addition, an algorithm is given for computing formal power series solutions of a D-finite system at apparent singularities.
Cite
@article{arxiv.1705.00838,
title = {Apparent Singularities of D-finite Systems},
author = {Shaoshi Chen and Manuel Kauers and Ziming Li and Yi Zhang},
journal= {arXiv preprint arXiv:1705.00838},
year = {2017}
}