Definition:Real Hyperbolic Cotangent/Definition 2

Definition

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

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

$\forall x \in \R_{\ne 0}: \coth x := \dfrac {\cosh x} {\sinh x}$

where:

$\sinh$ is the real hyperbolic sine

$\cosh$ is the real hyperbolic cosine

It is noted that at $x = 0$ we have that $\sinh x = 0$, 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

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $8.8$: Relationships among Hyperbolic Functions
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): hyperbolic function