BUILT-IN MATHEMATICA SYMBOL

WeierstrassPPrime

gives the derivative of the Weierstrass elliptic function

.

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

Evaluate numerically:

Series expansion:

Evaluate numerically:

Out[1]=

Out[1]=

Series expansion:

Out[1]=

Evaluate for complex arguments and invariants:

Evaluate to high precision:

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

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

WeierstrassPPrime automatically evaluates to simpler functions for certain parameters:

Conformal map from a triangle to the upper half-plane:

Map a triangle:

Uniformization of a generic elliptic curve

:

The parametrized uniformization:

Check the correctness of the uniformization:

Define Dixon trigonometric functions:

These functions are cubic generalizations of Cos and Sin:

Plot the Dixon trigonometric functions:

Series expansions of these functions:

Integrate expressions involving WeierstrassPPrime:

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

Use arbitrary-precision arithmetic to obtain a correct result:

Weierstrass functions are doubly periodic over the complex plane: