Difference between revisions of "Arcsinh"
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| − | The inverse hyperbolic sine function $\mathrm{arcsinh | + | The inverse hyperbolic sine function $\mathrm{arcsinh}$ is function is the [[inverse function]] of the [[sinh|hyperbolic sine]] function. It may be defined by |
| + | $$\mathrm{arcsinh}(z)=\log \left(z + \sqrt{1+z^2} \right),$$ | ||
| + | where $\log$ denotes the [[logarithm]]. | ||
<div align="center"> | <div align="center"> | ||
<gallery> | <gallery> | ||
File:Arcsinhplot.png|Plot of $\mathrm{arcsinh}$ on $[-10,10]$. | File:Arcsinhplot.png|Plot of $\mathrm{arcsinh}$ on $[-10,10]$. | ||
| − | File: | + | File:Complexarcsinhplot.png|[[Domain coloring]] of of $\mathrm{arcsinh}$. |
</gallery> | </gallery> | ||
</div> | </div> | ||
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=Properties= | =Properties= | ||
[[Derivative of arcsinh]]<br /> | [[Derivative of arcsinh]]<br /> | ||
| + | [[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.
Plot of $\mathrm{arcsinh}$ on $[-10,10]$.
Domain coloring of of $\mathrm{arcsinh}$.
Properties
Derivative of arcsinh
Antiderivative of arcsinh
