Built-in Mathematica Symbol

WeierstrassP

WeierstrassP[u, {g₂, g₃}]
gives the Weierstrass elliptic function

.

For certain special arguments, WeierstrassP automatically evaluates to exact values.

Evaluate numerically:

Series expansion:

Evaluate numerically:

Series expansion:

Evaluate for complex arguments and invariants:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

WeierstrassP threads element-wise over lists in its first argument:

WeierstrassP automatically evaluates to simpler functions for certain parameters:

Express roots of a cubic through WeierstrassP:

Uniformization of a generic elliptic curve

:

The parametrized uniformization:

Check the correctness of the uniformization:

Special solution of the Korteweg-de Vries equation:

The Korteweg-de Vries equation:

A high-precision check of the solution:

Plot of the solution:

Derivatives:

Integrate expressions involving WeierstrassP:

Machine-precision input is insufficient to give a correct result:

Use arbitrary-precision arithmetic to obtain a correct result:

Plot a doubly periodic function over the complex plane: