Definition:Order of Pole/Simple Pole

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Definition

Let $f: \C \to \C$ be a complex function.


Let $z_0 \in U \subset \C$ be such that $f$ is holomorphic in $U \setminus \set {z_0}$, with a pole at $z_0$.

Let the order of the pole at $z_0$ be $1$.

Then $z_0$ is a simple pole.


Sources