Definition:Hyperbolic Cotangent/Definition 4

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

 * Equivalence of Definitions of Hyperbolic Cotangent


 * Definition:Hyperbolic Sine
 * Definition:Hyperbolic Cosine
 * Definition:Hyperbolic Tangent
 * Definition:Hyperbolic Secant
 * Definition:Hyperbolic Cosecant