\weierp - LaTeX Symbol

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℘

\weierp

The \weierp symbol represents the Weierstrass elliptic function, which is a type of complex function used in various areas of mathematics, including number theory and algebraic geometry. It is named after the German mathematician Karl Weierstrass.

Examples

℘ (z; g_{2}, g_{3})

The Weierstrass elliptic function with invariants g_2 and g_3.

\weierp(z; g_2, g_3)

℘ (z) = \frac{1}{z ^{2}} + n \neq = 0 \sum (\frac{1}{( z - n ) ^{2}} - \frac{1}{n ^{2}})

Series representation of the Weierstrass elliptic function.

\weierp(z) = \frac{1}{z^2} + \sum_{n \neq 0} \left( \frac{1}{(z - n)^2} - \frac{1}{n^2} \right)

℘^{'} (z)^{2} = 4 ℘ (z)^{3} - g_{2} ℘ (z) - g_{3}

Differential equation satisfied by the Weierstrass elliptic function.

\weierp'(z)^2 = 4\weierp(z)^3 - g_2\weierp(z) - g_3