Definition:Inverse Hyperbolic Tangent/Complex/Definition 1

Definition
Let $\tanh: \C \to \C$ denote the hyperbolic tangent as defined on the set of complex numbers.

The inverse hyperbolic tangent is a multifunction defined as:


 * $\forall x \in \C: \tanh^{-1} \left({x}\right) = \left\{{y \in \C: x = \tanh \left({y}\right)}\right\}$

Also see

 * Equivalence of Definitions of Inverse Hyperbolic Tangent


 * Definition:Inverse Hyperbolic Sine
 * Definition:Inverse Hyperbolic Cosine
 * Definition:Inverse Hyperbolic Cotangent
 * Definition:Inverse Hyperbolic Secant
 * Definition:Inverse Hyperbolic Cosecant