On the real axis The function along the real axis. is real‐valued in the interval and . At , the function has logarithmic singularities. 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 . 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 . 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 vanishes identically. 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 .
