Zeros and poles
In complex analysis (a branch of mathematics), a pole is a certain type of singularity of a complex-valued function of a complex variable. It is the simplest type of non-removable singularity of such a function (see essential singularity). Technically, a point z0 is a pole of a function f if it is a zero of the function 1/f and 1/f is holomorphic (i.e. complex differentiable) in some neighbourhood of z0.
Zeros and poles - Wikipedia Jump to content From Wikipedia, the free encyclopedia Concept in complex analysis This article includes a list of references , related reading , or external links , but its sources remain unclear because it lacks inline citations . Please help improve this article by introducing more precise citations. ( May 2025 ) ( Learn how and when to remove this message ) Mathematical analysis → Complex analysis Complex analysis Complex numbers Real number Imaginary number Complex plane Complex conjugate Euler's formula Basic theory Argument principle Residue Essential singular
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