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

0,1

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

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

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

Example

0.79788456080286535587989211986876373695171726232986931533...

Mathematica

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

Prog

(Magma) pi:=Sqrt(2/Pi(RealField(110))); Reverse(Intseq(Floor(10^110*pi))); // Vincenzo Librandi, Jul 01 2017
(PARI) sqrt(2/Pi) \\ G. C. Greubel, Sep 23 2017

Crossrefs

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

Sequence in context: A345384 A199742 A258112 * A010729 A340220 A182688

Adjacent sequences: A076665 A076666 A076667 * A076669 A076670 A076671

Keyword

nonn,cons

Author

Zak Seidov, Oct 25 2002

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

Status

approved