Definition:Real Hyperbolic Cotangent/Definition 1

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


 * $\coth: \R_{\ne 0} \to \R$:


 * $\forall x \in \R_{\ne 0}: \coth x := \dfrac {e^x + e^{-x} } {e^x - e^{-x} }$

where it is noted that at $x = 0$:
 * $e^x - e^{-x} = 0$

and so $\coth x$ is not defined at that point.

Also see

 * Equivalence of Definitions of Real Hyperbolic Cotangent


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