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math.CO2005
Twenty combinatorial examples of asymptotics derived from multivariate generating functions
Robin Pemantle, Mark C. Wilson
Let $\{a_\rr : \rr \in (\Z^+)^d \}$ be a -dimensional array of numbers, for which the generating function $F(\zz) := \sum_\rr a_\rr \zz^\rr$ is meromorphic in a neighborhood of…
math.CO2005
When is 0.999... equal to 1?
R. Pemantle, C. Schneider
A doubly infinite sum, numerically evaluated at between 0.999 and 1.001, turns out to have a nice value.