\begin{definition}[Definition:Order of Entire Function/Definition 2]
Let $f: \C \to \C$ be an entire function.
Let $f$ be not identically zero.
The '''order''' $\alpha \in \closedint 0 {+\infty}$ of $f$ is the infimum of the $\beta \ge 0$ for which:
:$\ds \map \ln {\max_{\size z \mathop \le R} \size {\map f z} } = \map \OO {R^\beta}$
or $\infty$ if no such $\beta$ exists, where $\OO$ denotes big-O notation
The '''order''' of $0$ is $0$.
\end{definition}