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Experiments with a positivity-preserving operator. (English) Zbl 1157.05003

Summary: We consider some multivariate rational functions that have (or are conjectured to have) only positive coefficients in their series expansion. We consider an operator that preserves positivity of series coefficients, and apply the inverse of this operator to the rational functions. We obtain new rational functions that seem to have only positive coefficients, whose positivity would imply positivity of the original series, and that, in a certain sense, cannot be improved any further.

MSC:

05A15 Exact enumeration problems, generating functions
33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)