2D plots along the axes and unit circle

On the real axis

The function along the real axis. is real‐valued outside the interval .

The function along the real axis. The left graphic shows and the right graphic shows . In the interval , the function is purely imaginary. At , the function has a logarithmic singularity.

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

On the real axis at infinity

The function along the real 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 . For , the argument is piecewise constant.

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, is purely imaginary and the absolute value of the imaginary part is an asymtotically a decreasing function. At the point , 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 .

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 .