Definition:Order of Entire Function/Definition 3
Jump to navigation
Jump to search
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 $0$.