Definition:Hyperbolic Tangent

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


 * $\tanh: (X \subset \C) \to \C$:


 * $\displaystyle \tanh z := \dfrac {\sinh z}{\cosh z}$

where $\sinh$ is the hyperbolic sine and $\cosh$ is the hyperbolic cosine.

This function is defined everywhere in $\C$ that $\cosh z \ne 0$.

Also See

 * Hyperbolic Secant, a similar function.