Definition:Hyperbolic Cotangent/Definition 4

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Definition

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

$\coth: X \to \C$:
$\forall z \in X: \coth z := \dfrac 1 {\tanh z}$

where:

$\tanh$ is the hyperbolic tangent
$X = \set {z : z \in \C, \ \sinh z \ne 0}$
where $\sinh$ is the hyperbolic sine.


Also see


Sources