在复分析中，椭圆函数是复平面上的双周期亚纯函数。历史上，椭圆函数起初被视作椭圆积分之逆。

更明确地说，固定中的格（），亚纯函数是的椭圆函数，若且唯若对每个皆有（此即「双周期」的含义）。

根据复分析中的极值原理，全纯椭圆函数只能是常数函数，故非常数的椭圆函数必带极点。

标准的椭圆函数有两种，分别是雅可比椭圆函数及魏尔斯特拉斯椭圆函数。虽然雅可比椭圆函数较为古老，且与实际应用的关系更为直接，大多数现代作者在介绍基本理论时多采用魏尔斯特拉斯椭圆函数，因其函数形式更为简单，且可构造出所有的椭圆函数。Θ函数虽非双周期函数，但也能用来构造椭圆函数。

In complex analysis, an elliptic function is a meromorphic function that is periodic in two directions. Just as a periodic function of a real variable is defined by its values on an interval, an elliptic function is determined by its values on a fundamental parallelogram, which then repeat in a lattice. Such a doubly periodic function cannot be holomorphic, as it would then be a bounded entire function, and by Liouville's theorem every such function must be constant. In fact, an elliptic function must have at least two poles (counting multiplicity) in a fundamental parallelogram, as it is easy to show using the periodicity that a contour integral around its boundary must vanish, implying that the residues of any simple poles must cancel.