Difference between revisions of "Integral of inverse erf from 0 to 1"
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==Theorem== | ==Theorem== | ||
The following formula holds: | The following formula holds: | ||
| − | $$\displaystyle\int_0^1 \mathrm{erf}^{-1}(x) | + | $$\displaystyle\int_0^1 \mathrm{erf}^{-1}(x) \mathrm{d}x=\dfrac{1}{\sqrt{\pi}},$$ |
| + | where $\mathrm{erf}^{-1}$ denotes the [[inverse error function]] and $\pi$ denotes [[pi]]. | ||
==Proof== | ==Proof== | ||
Latest revision as of 04:46, 16 September 2016
Theorem
The following formula holds: $$\displaystyle\int_0^1 \mathrm{erf}^{-1}(x) \mathrm{d}x=\dfrac{1}{\sqrt{\pi}},$$ where $\mathrm{erf}^{-1}$ denotes the inverse error function and $\pi$ denotes pi.
