A178647 Decimal expansion of the fraction of a population falling within +- 1 standard deviation of the mean, assuming a normal distribution.
6, 8, 2, 6, 8, 9, 4, 9, 2, 1, 3, 7, 0, 8, 5, 8, 9, 7, 1, 7, 0, 4, 6, 5, 0, 9, 1, 2, 6, 4, 0, 7, 5, 8, 4, 4, 9, 5, 5, 8, 2, 5, 9, 3, 3, 4, 5, 3, 2, 0, 8, 7, 8, 1, 9, 7, 4, 7, 8, 8, 9, 0, 0, 4, 8, 5, 9, 8, 2, 8, 8, 3, 9, 7, 4, 4, 0, 9, 6, 5, 9, 0, 0, 1, 7, 6, 9, 8, 3, 6, 8, 1, 1, 2, 7, 8, 6, 5, 5, 0, 5, 6, 5, 4, 5
Offset: 0
Examples
0.6826894921370858971704650912640758449558259334532087819747889004859...
References
- Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 40, table 40:7:1 at page 387.
Links
- Rick L. Shepherd, Table of n, a(n) for n = 0..10000
- Eric Weisstein's World of Mathematics, Erf.
- Wikipedia, 68-95-99.7 rule.
Programs
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MATLAB
0.5*(1+erf(1/sqrt(2)))- 0.5*(1+erf(-1/sqrt(2)))
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Maple
erf(1/sqrt(2)) ; evalf(%) ; # R. J. Mathar, Mar 22 2016
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Mathematica
RealDigits[(1 + Erf[1/Sqrt@2])/2 - (1 + Erf[ -1/Sqrt@2])/2, 10, 111][[1]] (* Robert G. Wilson v, Jun 01 2010 *)
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PARI
(erfc(-1/sqrt(2))-erfc(1/sqrt(2)))/2 \\ Charles R Greathouse IV, Sep 04 2012
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PARI
1 - erfc(1/sqrt(2)) \\ Rick L. Shepherd, Mar 05 2014
Formula
Equals erf(1/sqrt(2)). - Jean-François Alcover, May 29 2013
Extensions
More terms from Robert G. Wilson v, Jun 01 2010
Edited by N. J. A. Sloane, Jun 07 2010