Definition:Real Inverse Hyperbolic Secant/Also known as

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Real Inverse Hyperbolic Secant: Also known as

The principal branch of the inverse hyperbolic secant is also known as the area hyperbolic secant, as it can be used, among other things, for evaluating areas of regions bounded by hyperbolas.

Some sources refer to it as hyperbolic arcsecant, but this is strictly a misnomer, as there is nothing arc related about an inverse hyperbolic secant.

In the real domain, $\mathsf{Pr} \infty \mathsf{fWiki}$ reserves the term area hyperbolic secant strictly for the principal branch, that is, for $\map \arsech x > 0$.