Definition:Order of Entire Function/Definition 3

Definition
Let $f: \C \to \C$ be an entire function. Let $f$ be non-constant.

The order $\alpha \in \left[{0 \,.\,.\, +\infty}\right]$ of $f$ is the limit superior:
 * $\displaystyle \limsup_{R \mathop \to \infty} \frac {\log \log \max_{\left\lvert{z}\right\rvert \le R} \left\lvert{f}\right\rvert} {\log R}$

The order of a constant function is $0$.

Also see

 * Equivalence of Definitions of Order of Entire Function