Definition:Hyperbolic Tangent/Definition 2

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


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


 * $\forall z \in X: \tanh z := \dfrac {\sinh z} {\cosh z}$

where:
 * $\sinh$ is the hyperbolic sine
 * $\cosh$ is the hyperbolic cosine
 * $X = \left\{{z : z \in \C, \ \cosh z \ne 0}\right\}$

Also see

 * Equivalence of Definitions of Hyperbolic Tangent


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