I am wondering for the following function $$ f(z) = \frac{e^{- (\log z)^2}}{\sqrt{z}}, $$ what kind of singularity does it have at $z=0$? I know that in the real line $f(x)$ is $C^\infty$, and I guess that $z=0$ is an isolated singularity and an essential singularity, but I do not have an idea how to show it.
2026-03-27 18:34:45.1774636485
Singularity of the following exponential function at z=0
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