A076668 Decimal expansion of sqrt(2/Pi).

7, 9, 7, 8, 8, 4, 5, 6, 0, 8, 0, 2, 8, 6, 5, 3, 5, 5, 8, 7, 9, 8, 9, 2, 1, 1, 9, 8, 6, 8, 7, 6, 3, 7, 3, 6, 9, 5, 1, 7, 1, 7, 2, 6, 2, 3, 2, 9, 8, 6, 9, 3, 1, 5, 3, 3, 1, 8, 5, 1, 6, 5, 9, 3, 4, 1, 3, 1, 5, 8, 5, 1, 7, 9, 8, 6, 0, 3, 6, 7, 7, 0, 0, 2, 5, 0, 4, 6, 6, 7, 8, 1, 4, 6, 1, 3, 8, 7, 2, 8, 6, 0, 6, 0

Offset: 0

Author

Zak Seidov, Oct 25 2002

Keywords

• nonn
• cons

Comments

This is the limit of (n+1)!!/n!!/n^(1/2) at n_even->inf.

Expected value of |x - mu|/sigma for normal distribution with mean mu and standard deviation sigma (i.e., the normalized mean absolute deviation). - Stanislav Sykora, Jun 30 2017

Examples

			0.79788456080286535587989211986876373695171726232986931533...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Harmann König, Carsten Schütt, and Nicole Tomczak-Jaegermann, Projection constants of symmetric spaces and variants of Khintchine's inequality, J. reine angew. Math. 511 (1999), pp. 1-42.
• Index entries for transcendental numbers

Crossrefs

Cf. A004730, A004731, A019727, A060294 (Buffon's constant 2/Pi), A092678 (probable error).

Programs

Magma

pi:=Sqrt(2/Pi(RealField(110))); Reverse(Intseq(Floor(10^110*pi))); // Vincenzo Librandi, Jul 01 2017

Mathematica

RealDigits[Sqrt[2/Pi],10,120][[1]] (* Harvey P. Dale, Feb 05 2012 *)

PARI

sqrt(2/Pi) \\ G. C. Greubel, Sep 23 2017

Formula

Equals A087197*A002193. - R. J. Mathar Feb 05 2009

Equals integral_{-infinity..infinity} (1-erf(x)^2)/2 dx. - Jean-François Alcover, Feb 25 2015

Extensions

More terms and better description from Benoit Cloitre and Michael Somos, Oct 29 2002

Leading zero removed, offset changed by R. J. Mathar, Feb 05 2009