Difference between revisions of "Weierstrass sigma"
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(Created page with "Let $\Lambda \subset \mathbb{C}$ be a lattice. The Weierstrass $\sigma$ function is defined by $$\sigma(z;\Lambda)=z \displaystyle\prod_{w \in \Lambda^*} \left( 1 - \dfrac...") |
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Let $\Lambda \subset \mathbb{C}$ be a [[lattice]]. The Weierstrass $\sigma$ function is defined by | Let $\Lambda \subset \mathbb{C}$ be a [[lattice]]. The Weierstrass $\sigma$ function is defined by | ||
| − | $$\sigma(z;\Lambda)=z \displaystyle\prod_{w \in \Lambda | + | $$\sigma(z;\Lambda)=z \displaystyle\prod_{w \in \Lambda \setminus \{0\}} \left( 1 - \dfrac{z}{w} \right) e^{\frac{z}{w}+\frac{1}{2}(\frac{z}{w})^2}.$$ |
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Revision as of 23:17, 21 May 2015
Let $\Lambda \subset \mathbb{C}$ be a lattice. The Weierstrass $\sigma$ function is defined by $$\sigma(z;\Lambda)=z \displaystyle\prod_{w \in \Lambda \setminus \{0\}} \left( 1 - \dfrac{z}{w} \right) e^{\frac{z}{w}+\frac{1}{2}(\frac{z}{w})^2}.$$
