arcsinh
The inverse hyperbolic sine function.
Syntax

arcsinh(x)

x
is a real or complex number

Description
arcsinh
is the inverse of the hyperbolic sine function. It is defined by
arcsinh(z) = ln(z + √(1 + z^2))
for all complex z
. arcsinh(x)
is real for all real x
.
Notes
This function is also called arsinh
(area hyperbolic sine) in the literature. Some authors claim that the name arcsinh
is a misnomer, but this depends crucially on how you view the connections between the trigonometric and the hyperbolic functions and their (restriction) inverses. One can argue that the name arcsinh
makes perfect sense.
Examples
arcsinh(0)
0
arcsinh(1)
0.88137358702
arcsinh(i)
1.57079632679⋅i