A quick look at the Weierstrass functions and inverses

Here is a quick look at the graphics for the Weierstrass functions and inverses. All of the following graphics use the half-periods .

The next pair of graphics shows the Weierstrass function over the complex ‐plane. The double periodicity of the function and the poles of order 2 are clearly visible.

The next pair of graphics shows the derivative of the Weierstrass function over the complex ‐plane. The double periodicity of the function and the poles of order 3 are clearly visible.

The next pair of graphics shows the Weierstrass zeta function over the complex ‐plane. The pseudo‐double periodicity of the function and the poles of order 1 are clearly visible.

The next pair of graphics shows the Weierstrass sigma function over the complex ‐plane.

The next three pairs of graphics show the associated Weierstrass sigma functions over the complex ‐plane.

The last pair of graphics shows the inverse of the Weierstrass function over the complex ‐plane. Compared with the direct function, it is relatively structureless.