Definition:Real Hyperbolic Cosecant/Definition 2

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


 * $\csch: \R_{\ne 0} \to \C$:


 * $\forall x \in \R_{\ne 0}: \csch x := \dfrac 1 {\sinh x}$

where $\sinh$ is the real hyperbolic sine.

It is noted that at $x = 0$ we have that $\sinh x = 0$, and so $\csch x$ is not defined at that point.

Also see

 * Equivalence of Definitions of Real Hyperbolic Cosecant


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