When can we detect that a P-finite sequence is positive?

Authors:
Manuel Kauers;Veronika Pillwein
Affiliations:
RISC, Johannes Kepler University, Linz (Austria);RISC, Johannes Kepler University, Linz (Austria)
Venue:
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Year:
2010

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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.