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A240723 Decimal expansion of a constant linked to a normal distribution inequality. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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
Sequence in context: A262974 A319757 A349220 * A254154 A121060 A230437
KEYWORD
nonn,cons
AUTHOR
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)