Definition:Hyperbolic Secant/Definition 2

Definition

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

$\sech: X \to \C$:

$\forall z \in X: \sech z := \dfrac 1 {\cosh z}$

where:

$\cosh$ is the hyperbolic cosine

$X = \set {z: z \in \C, \ \cosh z \ne 0}$

Also see

• Equivalence of Definitions of Hyperbolic Secant

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

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $8.9$: Relationships among Hyperbolic Functions
• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $2$: Functions, Limits and Continuity: The Elementary Functions: $5$
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: hyperbolic function

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