This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# WeierstrassP

 WeierstrassPgives the Weierstrass elliptic function .
• Mathematical function, suitable for both symbolic and numerical manipulation.
• gives the value of for which .
• For certain special arguments, WeierstrassP automatically evaluates to exact values.
• WeierstrassP can be evaluated to arbitrary numerical precision.
Evaluate numerically:
Series expansion:
Evaluate numerically:
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Series expansion:
 Out[1]=
 Scope   (6)
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:
 Applications   (3)
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: