Weierstrass elliptic function
= Weierstrass elliptic function
{c}
{title2=$\wp$}
{wiki}
For a <period lattice> $\Lambda\subset\mathbb C$, the Weierstrass elliptic function is the normally convergent lattice sum
$$
\wp_\Lambda(z)=\frac1{z^2}+\sum_{\omega\in\Lambda\setminus\{0\}}\left(\frac1{(z-\omega)^2}-\frac1{\omega^2}\right).
$$
It 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>.