Manuel Kauers, Veronika Pillwein,
"When can we detect that a P-finite sequence is positive?"
, in Stephen Watt: Proceedings of ISSAC'10, Seite(n) 195--202, 2010, ISBN: 978-1-4503-0150-3
When can we detect that a P-finite sequence is positive?
Sprache des Titels:
Proceedings of ISSAC'10
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.