I understand that meromorphic functions are functions that have poles at points which are isolated. My question is why are meromorphic functions defined like this? Do bad things happen if they weren't isolated?
2026-03-25 18:47:23.1774464443
Why are meromorphic functions defined on poles that are isolated?
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Yes, your speculation is correct: isolated singularities can be understood well, functions have Laurent expansions, etc., whether the singularity is removable, a pole, or essential. In contrast, at an accumulation point of poles (or essential singularities) we apparently have no good way to understand what a function might do.