If $f:\mathbb{C}\setminus\{z_0\}\to\mathbb{C}$ is an analytic function with an essential singularity at $z_0$, is there any elementary reason why there exists at least one complex value that the function takes infinitely often in any neighbourhood of $z_0$? The non-elementary reason is Picard's Theorem.
2026-03-26 01:27:36.1774488456
Range of analytic functions
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