BUILT-IN MATHEMATICA SYMBOL

WeierstrassZeta

gives the Weierstrass zeta function

.

WeierstrassZeta is not periodic and is therefore not strictly an elliptic function.

For certain special arguments, WeierstrassZeta 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:

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

WeierstrassZeta automatically evaluates to simpler functions for certain parameters:

The 2D equations of motion of two point-like vertices having closed trajectories:

Solve the equations numerically:

Plot the vortex trajectories:

Derivatives of WeierstrassZeta:

Antiderivative:

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

Use arbitrary-precision arithmetic to obtain a correct result:

Plot the quasi-doubly periodic WeierstrassZeta over the complex plane: