The inverse hyperbolic cotangent function.
xis a real or complex number
arccoth is the inverse of the hyperbolic cotangent function. For real numbers, the domain is ℝ ∖ [−1, 1]. It is defined by
arccoth(z) = ln((z + 1)/(z − 1)) / 2
for all complex
z. This formula is also used for real numbers in (−1, 1).
This function is also called
arcoth (area hyperbolic cotangent) in the literature. Some authors claim that the name
arccoth 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
arccoth makes perfect sense.
0.385968416453 − 1.57079632679⋅i