When can we decide that a P-finite sequence is positive?
Symbolic Computation
2010-05-05 v1
Abstract
We consider two algorithms which can be used for proving positivity of sequences that are defined by a linear recurrence equation with polynomial coefficients (P-finite sequences). Both algorithms have in common that while they do succeed on a great many examples, there is no guarantee for them to terminate, and they do in fact not terminate for every input. For some restricted classes of P-finite recurrence equations of order up to three we provide a priori criteria that assert the termination of the algorithms.
Cite
@article{arxiv.1005.0600,
title = {When can we decide that a P-finite sequence is positive?},
author = {Manuel Kauers and Veronika Pillwein},
journal= {arXiv preprint arXiv:1005.0600},
year = {2010}
}