Definition:Order of Entire Function/Definition 3

Definition

Let $f: \C \to \C$ be an entire function.

Let $f$ be non-constant.

The order $\alpha \in \closedint 0 {+\infty}$ of $f$ is the limit superior:

$\ds \limsup_{R \mathop \to \infty} \frac {\ds \ln \ln \max_{\cmod z \mathop \le R} \cmod f} {\ln R}$

The order of a constant function is $0$.

Also see

• Equivalence of Definitions of Order of Entire Function