\begin{definition}[Definition:Doubly Periodic Function]
Let $f: \C \to \C$ be a complex function. 
Then $f \left({z}\right)$ is a '''doubly-periodic function''' if there exist $\omega_1, \omega_2 \in \C$ such that:
: $(1): \quad \omega_1, \omega_2 \ne 0$
: $(2): \quad \dfrac {\omega_1} {\omega_2} \notin \R$
: $(3): \quad \forall z \in \C: f \left({z}\right) = f \left({z + \omega_1}\right) = f \left({z + \omega_2}\right)$
\end{definition}