OFFSET
0,1
COMMENTS
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...
LINKS
FORMULA
Solution to erf(x/sqrt(2)) = sqrt(1 - sqrt(2/Pi)).
EXAMPLE
0.597119659996365533437506365687405320339554413...
MATHEMATICA
Sqrt[2]*InverseErf[Sqrt[1 - Sqrt[2/Pi]]] // RealDigits[#, 10, 100]& // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Apr 11 2014
STATUS
approved