Difference between revisions of "Arccoth"

From specialfunctionswiki
Jump to: navigation, search
 
(5 intermediate revisions by the same user not shown)
Line 1: Line 1:
 +
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:Complex Coth.jpg|[[Domain coloring]] of [[analytic continuation]] of $\mathrm{arccoth}$.
+
File:Complexarccothplot.png|[[Domain coloring]] of $\mathrm{arccoth}$.
 
</gallery>
 
</gallery>
 
</div>
 
</div>
  
<center>{{:Inverse hyperbolic trigonometric functions footer}}</center>
+
==Properties==
 +
[[Derivative of arccoth]]<br />
 +
 
 +
==See also==
 +
[[Arccot]] <br />
 +
[[Cotangent]]<br />
 +
[[Coth]]<br />
 +
 
 +
{{:Inverse hyperbolic trigonometric functions footer}}
  
 
[[Category:SpecialFunction]]
 
[[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.

Properties

Derivative of arccoth

See also

Arccot
Cotangent
Coth

Inverse hyperbolic trigonometric functions