= Simply periodic function
{title2=$\operatorname{Per}(f)=\omega\mathbb Z$}
A <nonconstant> <meromorphic function> on the <complex plane> is a <simply periodic function> when its <period group of a function> is generated by one nonzero <complex number>: $\operatorname{Per}(f)=\omega\mathbb Z$. It repeats in one independent complex direction.
For example, $f(z)=e^z$ satisfies $e^{z+\omega}=e^z$ exactly when $e^\omega=1$, so its periods are $2\pi i\mathbb Z$. A doubly periodic <elliptic function> instead has a <period lattice> generated by two real-linearly independent <complex numbers>. Single periodicity alone imposes no algebraic addition law.
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