 Weierstrass elliptic function

For a period lattice $\Lambda \subset \mathbb{C}$, the Weierstrass elliptic function is the normally convergent lattice sumIt is an even elliptic function with a double pole of principal part $(z-\omega {)}^{-2}$ and zero residue at every point $\omega$ of the period lattice.

The Weierstrass elliptic function is a fundamental object in the theory of elliptic functions, which are special functions that have a periodic nature in two directions. These functions are used extensively in various fields of mathematics, including complex analysis, algebraic geometry, and number theory.