Definition:Order of Pole/Simple Pole

Definition

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

Let $x \in U \subset \C$ be such that $f$ is analytic in $U \setminus \left\{{x}\right\}$, with a pole at $x$.

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

Then $x$ is a simple pole.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Entry: simple pole