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

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

2010-05-04

arxiv.org/abs/1005.0600v1

Computer Science

Symbolic Computation

Scientific paper

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.

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