Algosim documentation: arcsech

arcsech

The inverse hyperbolic secant function.

Syntax

Description

Image 1

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].

Notes

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.

Examples

arcsech(1/e)
1.65745445415
arcsech(1)
0
arcsech(2)
1.0471975512⋅i
arcsech(−1)
3.14159265359⋅i
arcsech(i)
0.88137358702 − 1.57079632679⋅i

See also