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 \(f\).