Definition:Hyperbolic Tangent/Definition 3

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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


Sources