Difference between revisions of "Arcsinh"

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The inverse hyperbolic sine function $\mathrm{arcsinh} \colon \mathbb{R} \rightarrow \mathbb{R}$ function is the [[inverse function]] of the [[sinh|hyperbolic sine]] function.
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The inverse hyperbolic sine function $\mathrm{arcsinh}$ is function is the [[inverse function]] of the [[sinh|hyperbolic sine]] function. It may be defined by
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$$\mathrm{arcsinh}(z)=\log \left(z + \sqrt{1+z^2} \right),$$
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where $\log$ denotes the [[logarithm]].
  
 
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File:Arcsinhplot.png|Plot of $\mathrm{arcsinh}$ on $[-10,10]$.
 
File:Arcsinhplot.png|Plot of $\mathrm{arcsinh}$ on $[-10,10]$.
File:Complex ArcSinh.jpg|[[Domain coloring]] of [[analytic continuation]] of $\mathrm{arcsinh}$.
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File:Complexarcsinhplot.png|[[Domain coloring]] of of $\mathrm{arcsinh}$.
 
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=Properties=
 
=Properties=
 
[[Derivative of arcsinh]]<br />
 
[[Derivative of arcsinh]]<br />
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[[Antiderivative of arcsinh]]<br />
  
 
=See Also=
 
=See Also=

Latest revision as of 23:28, 11 December 2016

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

Properties

Derivative of arcsinh
Antiderivative of arcsinh

See Also

Arcsin
Sine
Sinh

References

Abramowitz&Stegun

Inverse hyperbolic trigonometric functions