Definition:Real Hyperbolic Cosecant/Definition 2

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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


Sources