Difference between revisions of "Inverse error function"
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Revision as of 04:45, 16 September 2016
The inverse error function is the inverse function of the error function. We denote it by writing $\mathrm{erf}^{-1}$.
Graph of $\mathrm{erf}^{-1}$.
Properties
Derivative of inverse error function
Antiderivative of inverse error function
Integral of inverse erf from 0 to 1
Theorem: The following formula holds: $$\displaystyle\int_0^1 \log(\mathrm{erf}^{-1}(x)) dx = \left( \dfrac{\gamma}{2} + \log(2) \right),$$ where $\mathrm{erf}^{-1}$ denotes the inverse error function, $\log$ denotes the logarithm, and $\gamma$ denotes the Euler-Mascheroni constant.
Proof: █
