2D plots along the axes and unit circle

On the real axis

The function along the real axis. is real‐valued in for . At , the function has a square root branch point.

The function along the real axis. The left graphic shows and the right graphic shows .

The absolute value and the argument of along the real axis. The left graphic shows and the right graphic shows . The argument is piecewise constant for .

On the real axis at infinity

The function along the real axis. The left graphic shows and the right graphic shows . The imaginary part is piecewise constant on the real axis. At , the function has a logarithmic singularity.

The absolute value and the argument of along the imaginary axis. The left graphic shows and the right graphic shows . The argument is constant for .

On the imaginary axes

The real part and the imaginary part of along the imaginary axis. The left graphic shows and the right graphic shows . Along the imaginary axis, the imaginary part is piecewise constant.

The absolute value and the argument of along the imaginary axis. The left graphic shows and the right graphic shows .

On the imaginary axis at infinity

The function along the imaginary axis. The left graphic shows and the right graphic shows .

The absolute value and the argument of along the imaginary axis. The left graphic shows and the right graphic shows .

On the unit circle

The real part and the imaginary part of on the unit circle. The left graphic shows and the right graphic shows .

The absolute value and the argument of on the unit circle. The left graphic shows and the right graphic shows .