Weierstrass sigma

Let $\Lambda \subset \mathbb{C}$ be a lattice. The Weierstrass $\sigma$ function is defined by $$\sigma(z;\Lambda)=z \displaystyle\prod_{w \in \Lambda^*} \left( 1 - \dfrac{z}{w} \right) e^{\frac{z}{w}+\frac{1}{2}(\frac{z}{w})^2},$$ where $\Lambda^*=\Lambda \setminus \{0\}$.