Difference between revisions of "Arccoth"
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| − | [[ | + | The inverse hyperbolic cotangent $\mathrm{arccoth}$ is the [[inverse function]] of the [[coth|hyperbolic cotangent]] function. It may be defined by the following formula: |
| − | + | $$\mathrm{arccoth}(z)=\mathrm{arctanh} \left( \dfrac{1}{z} \right),$$ | |
| + | where $\mathrm{arctanh}$ denotes the [[arctanh|inverse hyperbolic tangent]]. | ||
<div align="center"> | <div align="center"> | ||
<gallery> | <gallery> | ||
File:Arccoth.png|Graph of $\mathrm{arccoth}$ on $(-\infty,-1) \bigcup (1,\infty)$. | File:Arccoth.png|Graph of $\mathrm{arccoth}$ on $(-\infty,-1) \bigcup (1,\infty)$. | ||
| − | File: | + | File:Complexarccothplot.png|[[Domain coloring]] of $\mathrm{arccoth}$. |
</gallery> | </gallery> | ||
</div> | </div> | ||
| + | |||
| + | ==Properties== | ||
| + | [[Derivative of arccoth]]<br /> | ||
| + | |||
| + | ==See also== | ||
| + | [[Arccot]] <br /> | ||
| + | [[Cotangent]]<br /> | ||
| + | [[Coth]]<br /> | ||
| + | |||
| + | {{:Inverse hyperbolic trigonometric functions footer}} | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 01:40, 16 September 2016
The inverse hyperbolic cotangent $\mathrm{arccoth}$ is the inverse function of the hyperbolic cotangent function. It may be defined by the following formula: $$\mathrm{arccoth}(z)=\mathrm{arctanh} \left( \dfrac{1}{z} \right),$$ where $\mathrm{arctanh}$ denotes the inverse hyperbolic tangent.
Graph of $\mathrm{arccoth}$ on $(-\infty,-1) \bigcup (1,\infty)$.
Domain coloring of $\mathrm{arccoth}$.
