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One way to try to give a value $S$ to a divergent series $\sum_{n=1}^\infty a_n$ is with a smooth cutoff function: $$ S = \lim_{N\to\infty}\sum_{n=1}^\infty a_n \eta\left(\frac{n}{N}\right) $$ where $\...

In my research I have come across a divergent asymptotic series $\sum_{n =0}^\infty a_n f_n(x)$ that formally solves a certain fairly simple nonlinear second-order ODE but does not seem to correspond ...

UPDATE. I am now making this a CW in the hope someone can improve the content of this question and/or correct the text. This is a concise version of this math.SE question of mine. I've got an answer ...