Definition:Order of a Zero
From ProofWiki
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.
