It seems the pole of the logarithmic function is special. Can we assign an order to this pole? Is it a pole of zeroth order?
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The logarithm cannot even be defined as an analytic function in a (punctured) neighborhood of $z=0$. Please clarify the question. – Martin R Nov 01 '19 at 11:07
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2It is not a pole, it is a branch point – George C Nov 01 '19 at 11:29
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Does this answer your question? Type of singularity of $\log z$ at $z=0$ – Yodo Nov 28 '22 at 15:26