arccsch
The inverse hyperbolic cosecant function.
Syntax

arccsch(x)

x
is a real or complex number

Description
arccsch
is the inverse of the hyperbolic cosecant function. For real numbers, the domain is ℝ ∖ {0}. It is defined by
arccsch(z) = ln(1/z + √(1 + 1/z^2))
for all complex nonzero z
.
Notes
This function is also called arcsch
(area hyperbolic cosecant) in the literature. Some authors claim that the name arccsch
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 arccsch
makes perfect sense.
Examples
arccsch(1)
0.88137358702
arccsch(−π)
−0.313165880451
arccsch(i)
−1.57079632679⋅i