Definition:Hyperbolic Tangent/Definition 3

Definition
The hyperbolic tangent function is defined on the complex numbers as:


 * $\tanh: X \to \C$:


 * $\forall z \in X: \tanh z := \dfrac {e^{2 z} - 1} {e^{2 z} + 1}$

where:
 * $X = \left\{{z : z \in \C, \ e^{2 z} + 1 \ne 0}\right\}$

Also see

 * Equivalence of Definitions of Hyperbolic Tangent


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