Difference between revisions of "Antiderivative of inverse error function"
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(Created page with "==Theorem== The following formula holds: $$\displaystyle\int \mathrm{erf}^{-1}(x) dx = -\dfrac{e^{-[\mathrm{erf}^{-1}(x)]^2}}{\sqrt{\pi}}.$$ ==Proof== ==References== Cate...") |
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==Theorem== | ==Theorem== | ||
The following formula holds: | The following formula holds: | ||
| − | $$\displaystyle\int \mathrm{erf}^{-1}(x) | + | $$\displaystyle\int \mathrm{erf}^{-1}(x) \mathrm{d}x = -\dfrac{\exp \left( {-[\mathrm{erf}^{-1}(x)]^2} \right) }{\sqrt{\pi}},$$ |
| + | where $\mathrm{erf}^{-1}$ denotes the [[inverse error function]], $\exp$ denotes the [[exponential]], and $\pi$ denotes [[pi]]. | ||
==Proof== | ==Proof== | ||
Revision as of 04:43, 16 September 2016
Theorem
The following formula holds: $$\displaystyle\int \mathrm{erf}^{-1}(x) \mathrm{d}x = -\dfrac{\exp \left( {-[\mathrm{erf}^{-1}(x)]^2} \right) }{\sqrt{\pi}},$$ where $\mathrm{erf}^{-1}$ denotes the inverse error function, $\exp$ denotes the exponential, and $\pi$ denotes pi.
