Definition:Periodic Function/Complex

Definition
Let $f: \C \to \C$ be a complex function.

Then $f$ is periodic :
 * $\exists L \in \C_{\ne 0}: \forall x \in \C: \map f x = \map f {x + L}$

Also see

 * General Periodicity Property: after every distance $L$, the function $f$ repeats itself.