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2D plots along the axes and unit circle On the real axis The function  along the real axis.  is real‐valued in the interval  . At  , the function  has a logarithmic singularity. The function  along the real axis. The left graphic shows  and the right graphic shows  . In the interval  the function  is purely imaginary and the real part vanishes identically. The absolute value and the argument of  along the real axis. The left graphic shows  and the right graphic shows  . For  and  , 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, the real part of  is a decreasing function and 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  .
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