elliptic function

An elliptic function is an analytic function from $\mathbb{C}$ to $\mathbb{C}$ which is doubly periodic. That is, for two independent values of the complex number $w$, the functions $f(z)$ and $f(w + z)$ are the same.
It can also be regarded as the inverse function to certain integrals (called elliptic integrals) of the form where $R$ is a polynomial of degree 3 or 4.