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How to correctly renormalize this function at the pole $x=1$? Evaluating: $\sum_{n=1}^{\infty} e^{e^n}$
So I was considering the divergent everywhere but 0 power series
$$ f(x) = \sum_{n=0}^{\infty} e^{e^n} x^n $$
Now one can do the following "questionable" manipulation
$$ f(x) = \sum_{n=0}^{\...
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