Weierstraß ℘-function

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The Weierstraß ℘-function is defined [1]

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \weierp(z;\Lambda)=\frac1{z^2} \sum_{\omega\in\Lambda}^{\omega\ne0} \left[ \frac1{(z-\omega)^2}-\frac1{\omega^2} \right]}

for and a lattice

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Lambda=\{m\omega_1+n\omega_2|m,n\in\mathbb Z \}}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \omega_1,\omega_2\in\mathbb C\backslash\{0\}} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathfrak{Im}(\omega_1/\omega_2)>0} .

  1. ↑ Joseph H. Silverman. Advanced Topics in the Arithmetic of Elliptic Curves. Springer, 1994, p. 6.