Definition:Hyperbolic Secant/Definition 1

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


 * $\operatorname{sech}: X \to \C$:


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

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

Also see

 * Equivalence of Definitions of Hyperbolic Secant


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