Definition:Order of Zero

Definition
Let $f : \C \supseteq U \to \C$ be an analytic function.

Suppose $x \in U$ such that $f(x) = 0$.

The least $n \in \N$ such that $f^{(n)}(x) \neq 0$ is called the order of the zero at $x$.

If the zero has order $1$ it is called simple.