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

Author

Joost de Winter, May 31 2010

Keywords

• nonn
• cons

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.

Crossrefs

Cf. A110894 (2sigma), A270712 (3sigma).

Programs

MATLAB

0.5*(1+erf(1/sqrt(2)))- 0.5*(1+erf(-1/sqrt(2)))

Maple

erf(1/sqrt(2)) ; evalf(%) ; # R. J. Mathar, Mar 22 2016

Mathematica

RealDigits[(1 + Erf[1/Sqrt@2])/2 - (1 + Erf[ -1/Sqrt@2])/2, 10, 111][[1]] (* Robert G. Wilson v, Jun 01 2010 *)

PARI

(erfc(-1/sqrt(2))-erfc(1/sqrt(2)))/2 \\ Charles R Greathouse IV, Sep 04 2012

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