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Decimal expansion of a constant linked to a normal distribution inequality.
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%I #7 Apr 15 2014 03:06:29

%S 5,9,7,1,1,9,6,5,9,9,9,6,3,6,5,5,3,3,4,3,7,5,0,6,3,6,5,6,8,7,4,0,5,3,

%T 2,0,3,3,9,5,5,4,4,1,3,0,4,4,5,8,4,4,8,9,5,8,5,5,6,9,1,3,0,1,1,8,3,3,

%U 7,4,6,3,2,4,8,0,8,2,6,2,1,1,6,7,5,7,8,5,1,7,8,5,6,0,3,9,1,8,8,5

%N Decimal expansion of a constant linked to a normal distribution inequality.

%C The inequality (x^2+1)*N(x)+x*n(x)-(x*N(x)+n(x))^2 > N(x)^2, where n(x) is the normal PDF n(0,1)(x) and N(x) the normal CDF N(0,1)(x), holds for every x such that |x| < 0.5971...

%H MathOverflow, <a href="http://mathoverflow.net/questions/135593">A Normal Distribution Inequality</a>

%F Solution to erf(x/sqrt(2)) = sqrt(1 - sqrt(2/Pi)).

%e 0.597119659996365533437506365687405320339554413...

%t Sqrt[2]*InverseErf[Sqrt[1 - Sqrt[2/Pi]]] // RealDigits[#, 10, 100]& // First

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Apr 11 2014