Definition:Hyperbolic Tangent/Definition 3

Definition

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

$\tanh: X \to \C$:

$\forall z \in X: \tanh z := \dfrac {e^{2 z} - 1} {e^{2 z} + 1}$

where:

$X = \set {z: z \in \C, \ e^{2 z} + 1 \ne 0}$

Also see

• Equivalence of Definitions of Hyperbolic Tangent

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

Sources

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