Experiments with a Positivity-Preserving Operator

Abstract

We consider some multivariate rational functions that have (orare conjectured to have) only positive coefficients in their seriesexpansion. We consider an operator that preserves positivityof series coefficients, and apply the inverse of this operator tothe rational functions. We obtain new rational functions thatseem to have only positive coefficients, whose positivity wouldimply positivity of the original series, and that, in a certain sense,cannot be improved any further.