\begin{definition}[Definition:Order of Entire Function/Definition 1]
Let $f: \C \to \C$ be an entire function.
The '''order''' $\alpha \in \closedint 0 {+\infty}$ of $f$ is the infimum of the $\beta \ge 0$ for which:
:$\map f z = \map \OO {\map \exp {\size z^\beta} }$
or $\infty$ if no such $\beta$ exists, where $\OO$ denotes big-O notation.
\end{definition}