Computing closed form solutions of integrable connections

@inproceedings{Barkatou2012ComputingCF,
title={Computing closed form solutions of integrable connections},
author={M. Barkatou and T. Cluzeau and Carole El Bacha and Jacques-Arthur Weil},
booktitle={ISSAC},
year={2012}
}

We present algorithms for computing rational and hyperexponential solutions of linear D-finite partial differential systems written as integrable connections. We show that these types of solutions can be computed recursively by adapting existing algorithms handling ordinary linear differential systems. We provide an arithmetic complexity analysis of the algorithms that we develop. A Maple implementation is available and some examples and applications are given.