Definition:Real Hyperbolic Secant/Definition 2

Definition

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

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $8.9$: Relationships among Hyperbolic Functions
• 1972: Frank Ayres, Jr. and J.C. Ault: Theory and Problems of Differential and Integral Calculus (SI ed.) ... (previous) ... (next): Chapter $15$: Differentiation of Hyperbolic Functions: Definition of Hyperbolic Functions
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): hyperbolic function

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