Definition:Real Hyperbolic Tangent/Definition 1

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


 * $\tanh: \R \to \R$:


 * $\forall x \in \R: \tanh x := \dfrac {e^z - e^{-x} } {e^z + e^{-x} }$

Also see

 * Equivalence of Definitions of Real Hyperbolic Tangent


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