arccsch
The inverse hyperbolic cosecant function.
Syntax
-
arccsch(x)-
xis 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 non-zero 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