A240723 Decimal expansion of a constant linked to a normal distribution inequality.

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, 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, 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

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

Table of n, a(n) for n=0..99.

MathOverflow, A Normal Distribution Inequality

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

Sequence in context: A262974 A319757 A349220 * A254154 A121060 A230437

Adjacent sequences: A240720 A240721 A240722 * A240724 A240725 A240726

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 11 2014

Status

approved