Definition:Elliptic Function

Definition
Let $\ds \map y x = \int_0^x \dfrac {\d t} {\sqrt {\map P t} }$ be an elliptic integral, where $\map P t$ is a polynomial of degree $3$ or $4$.

Consider the inverse of $\map y x$:
 * $x = \map \phi y$

Then $\phi$ is an elliptic function.

Also see

 * Meromorphic Function is Elliptic iff Doubly Periodic