Periodicity of Complex Functions

Definition: Periodicity of Complex Functions

A complex function \(f: \mathcal{D} \subseteq \mathbb{C} \to \mathbb{C}\) is periodic if there exists some \(P \in \mathbb{C}\) such that

\[ f(z + P) = f(z) \qquad \forall z \in \mathcal{D}. \]

The number \(P\) is called a period of \(f\).