Difference between revisions of "Integral of inverse erf from 0 to 1"

From specialfunctionswiki
Jump to: navigation, search
(Created page with "==Theorem== The following formula holds: $$\displaystyle\int_0^1 \mathrm{erf}^{-1}(x) dx=\dfrac{1}{\sqrt{\pi}}.$$ ==Proof== ==References== Category:Theorem Category:U...")
 
Line 1: Line 1:
 
==Theorem==
 
==Theorem==
 
The following formula holds:
 
The following formula holds:
$$\displaystyle\int_0^1 \mathrm{erf}^{-1}(x) dx=\dfrac{1}{\sqrt{\pi}}.$$
+
$$\displaystyle\int_0^1 \mathrm{erf}^{-1}(x) \mathrm{d}x=\dfrac{1}{\sqrt{\pi}}.$$
  
 
==Proof==
 
==Proof==

Revision as of 04:46, 16 September 2016

Theorem

The following formula holds: $$\displaystyle\int_0^1 \mathrm{erf}^{-1}(x) \mathrm{d}x=\dfrac{1}{\sqrt{\pi}}.$$

Proof

References