Definition:Order of Pole/Simple Pole

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.