Difference between revisions of "Arcsinh"
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| − | [[ | + | __NOTOC__ |
| + | 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]]. | ||
| − | <center>{{:Inverse hyperbolic trigonometric functions footer}} | + | <div align="center"> |
| + | <gallery> | ||
| + | File:Arcsinhplot.png|Plot of $\mathrm{arcsinh}$ on $[-10,10]$. | ||
| + | File:Complexarcsinhplot.png|[[Domain coloring]] of of $\mathrm{arcsinh}$. | ||
| + | </gallery> | ||
| + | </div> | ||
| + | |||
| + | =Properties= | ||
| + | [[Derivative of arcsinh]]<br /> | ||
| + | [[Antiderivative of arcsinh]]<br /> | ||
| + | |||
| + | =See Also= | ||
| + | [[Arcsin]] <br /> | ||
| + | [[Sine]] <br /> | ||
| + | [[Sinh]] | ||
| + | |||
| + | =References= | ||
| + | [http://dualaud.net/specialfunctionswiki/abramowitz_and_stegun-1.03/page_86.htm Abramowitz&Stegun] | ||
| + | |||
| + | {{:Inverse hyperbolic trigonometric functions footer}} | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
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
