Definition:Complex Inverse Hyperbolic Cotangent/Also known as

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Complex Inverse Hyperbolic Cotangent: Also known as

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

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

In the complex plane, $\mathsf{Pr} \infty \mathsf{fWiki}$ reserves the term area hyperbolic cotangent strictly for the principal branch.