Definition:Hyperbolic Cotangent/Definition 3

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


 * $\coth: X \to \C$:


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

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

Also see

 * Equivalence of Definitions of Hyperbolic Cotangent


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