Difference between revisions of "Arccosh"

From specialfunctionswiki
Jump to: navigation, search
(Properties)
 
(6 intermediate revisions by the same user not shown)
Line 1: Line 1:
 +
The inverse hyperbolic cosine function $\mathrm{arccosh}$ is the [[inverse function]] of the [[hyperbolic cosine]] function. It may be defined by
 +
$$\mathrm{arccosh}(z)=\log \left(z + \sqrt{1+z^2} \right),$$
 +
where $\log$ denotes the [[logarithm]].
 +
 
<div align="center">
 
<div align="center">
 
<gallery>
 
<gallery>
 
File:Arccoshplot.png|Graph of $\mathrm{arccos}$ on $[1,10]$.
 
File:Arccoshplot.png|Graph of $\mathrm{arccos}$ on $[1,10]$.
File:Complex ArcCosh.jpg|[[Domain coloring]] of [[analytic continuation]] of $\mathrm{arccosh}$.
+
File:Complexarccoshplot.png|[[Domain coloring]] of $\mathrm{arccosh}$.
 
</gallery>
 
</gallery>
 
</div>
 
</div>
 +
 +
=Properties=
 +
[[Derivative of arccosh]] <br />
 +
[[Antiderivative of arccosh]]<br />
 +
 +
=See Also=
 +
[[Arccos]] <br />
 +
[[Cosh]] <br />
 +
[[Cosine]] <br />
  
 
{{:Inverse hyperbolic trigonometric functions footer}}
 
{{:Inverse hyperbolic trigonometric functions footer}}
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Latest revision as of 23:42, 11 December 2016

The inverse hyperbolic cosine function $\mathrm{arccosh}$ is the inverse function of the hyperbolic cosine function. It may be defined by $$\mathrm{arccosh}(z)=\log \left(z + \sqrt{1+z^2} \right),$$ where $\log$ denotes the logarithm.

Properties

Derivative of arccosh
Antiderivative of arccosh

See Also

Arccos
Cosh
Cosine

Inverse hyperbolic trigonometric functions