The inverse hyperbolic secant function.
xis a real or complex number
arcsech is the inverse of the restriction of the hyperbolic secant function to [0, ∞). For real numbers, the domain is (0, 1]. It is defined by
arcsech(z) = ln(1/z + √(1/z + 1) ⋅ √(1/z − 1))
for all complex
z. This formula is also used for real numbers outside [0, 1].
This function is also called
arsech (area hyperbolic secant) in the literature. Some authors claim that the name
arcsech 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
arcsech makes perfect sense.
0.88137358702 − 1.57079632679⋅i