Definition:Real Hyperbolic Cotangent/Definition 3
Jump to navigation
Jump to search
Definition
The real hyperbolic cotangent function is defined on the real numbers as:
- $\coth: \R_{\ne 0} \to \R$:
- $\forall x \in \R_{\ne 0}: \coth x := \dfrac 1 {\tanh x}$
where $\tanh$ is the real hyperbolic tangent.
It is noted that at $x = 0$ we have that $\tanh x = 0$, and so $\coth x$ is not defined at that point.
Also see
- Definition:Real Hyperbolic Sine
- Definition:Real Hyperbolic Cosine
- Definition:Real Hyperbolic Tangent
- Definition:Real Hyperbolic Secant
- Definition:Real Hyperbolic Cosecant
Sources
- 1972: Frank Ayres, Jr. and J.C. Ault: Theory and Problems of Differential and Integral Calculus (SI ed.) ... (previous) ... (next): Chapter $15$: Differentiation of Hyperbolic Functions: Definition of Hyperbolic Functions