Definition:Hyperbolic Secant/Real

Definition

Definition 1

The real hyperbolic secant function is defined on the real numbers as:

$\sech: \R \to \R$:

$\forall x \in \R: \sech z := \dfrac 2 {e^x + e^{-x} }$

Definition 2

The real hyperbolic secant function is defined on the real numbers as:

$\sech: \R \to \R$:

$\forall x \in \R: \sech x := \dfrac 1 {\cosh x}$

where $\cosh$ is the real hyperbolic cosine.

Also see

• Equivalence of Definitions of Real Hyperbolic Secant

• Definition:Real Hyperbolic Sine
• Definition:Real Hyperbolic Cosine
• Definition:Real Hyperbolic Tangent
• Definition:Real Hyperbolic Cotangent
• Definition:Real Hyperbolic Cosecant

• Results about the hyperbolic secant function can be found here.

Sources

• Weisstein, Eric W. "Hyperbolic Secant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HyperbolicSecant.html