|
|
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
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|