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 ArcSinh

2D plots along the axes and unit circle

On the real axis

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

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

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.

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 in the interval and the absolute value of the imaginary part is constant outside the interval .

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 . 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 .

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 .