If the set $P$ of periods of a meromorphic function $f:\mathbb{C}\to \mathbb{C}$ is of the form $\omega \mathbb{Z}$, then we say $f$ is simply periodic. Examples of simply periodic functions are ($\sin (z),\cos (z),\tan (z),\text{cotan}(z),e^z,\dots$)

If $f$ is periodic but not simply periodic, then it is ==1;;doubly periodic, and $P={\omega }_1\mathbb{Z}+{\omega }_2\mathbb{Z}$ for ${\omega }_1,{\omega }_2\in {\mathbb{C}}^{\ast }$.