Optimal truncation
= Optimal truncation
A divergent <asymptotic expansion> should usually be stopped near its smallest term rather than summed indefinitely. For factorial terms $n!z^{-n}$ the cutoff has $n=|z|+O(1)$. This exposes exponentially small contributions and the <Stokes phenomenon>. The smallest term alone does not always bound the remainder, especially when a saddle meets a pole.