Definition:Hyperbolic Tangent/Definition 2

Definition

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

$\tanh: X \to \C$:

$\forall z \in X: \tanh z := \dfrac {\sinh z} {\cosh z}$

where:

$\sinh$ is the hyperbolic sine

$\cosh$ is the hyperbolic cosine

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

Also see

• Equivalence of Definitions of Hyperbolic Tangent

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

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $2$: Functions, Limits and Continuity: The Elementary Functions: $5$
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): hyperbolic function
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): hyperbolic functions
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): hyperbolic functions

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