A meromorphic doubly-periodic function defined on the complex plane such that f(z+ma+nb) = f(z) for all integers m, n, where a/b is not real. Note that such an elliptic function defines a meromorphic function on the elliptic curve ℂ/Λ‎, where Λ‎ denotes the lattice aℤ + bℤ.

Note further by Liouville’s theorem that holomorphic elliptic functions are constant. Elliptic functions became of interest as a consequence of elliptic integrals.