Difference between revisions of "Weierstrass sigma"

From specialfunctionswiki
Jump to: navigation, search
(Created page with "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...")
 
Line 1: Line 1:
 
Let $\Lambda \subset \mathbb{C}$ be a [[lattice]]. The Weierstrass $\sigma$ function is defined by
 
Let $\Lambda \subset \mathbb{C}$ be a [[lattice]]. The Weierstrass $\sigma$ function is defined by
$$\sigma(z;\Lambda)=z \displaystyle\prod_{w \in \Lambda^*} \left( 1 - \dfrac{z}{w} \right) e^{\frac{z}{w}+\frac{1}{2}(\frac{z}{w})^2},$$
+
$$\sigma(z;\Lambda)=z \displaystyle\prod_{w \in \Lambda \setminus \{0\}} \left( 1 - \dfrac{z}{w} \right) e^{\frac{z}{w}+\frac{1}{2}(\frac{z}{w})^2}.$$
where $\Lambda^*=\Lambda \setminus \{0\}$.
 

Revision as of 23:17, 21 May 2015

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