A134469 Decimal expansion of -zeta(1/2)/sqrt(2*Pi).

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

Offset

0,1

Comments

This number is the limiting expected overshoot over a boundary for the sum of independent and identically distributed normal variables with unit variance, as their positive mean approaches zero. It has applications in sequential analysis.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Joseph T. Chang and Yuval Peres, Ladder heights, Gaussian random walks and the Riemann zeta function, Annals of Probability, 25(2) (1997) 787-802.

Alain Comtet and Satya N. Majumdar, Precise Asymptotics for a Random Walker’s Maximum, J. Stat. Mech. Theor. Exp. 06 (2005) P06013, arXiv:cond-mat/0506195 [cond-mat.stat-mech], 2005.

Hans J. H. Tuenter, Overshoot in the Case of Normal Variables: Chernoff's Integral, Latta's Observation and Wijsman's Sum, Sequential Analysis, 26(4) (2007) 481-488.

Robert A. Wijsman, Overshoot in the Case of Normal Variables, Sequential Analysis, 23(2):275-284, 2004.

Formula

-zeta(1/2)/sqrt(2*Pi)= A059750/A019727.

Example

0.58259715793901067020517716418763115472909387019865...

Maple

Digits:=100; evalf(-Zeta(1/2)/sqrt(2*Pi));

Mathematica

RealDigits[-Zeta[1/2]/Sqrt[2*Pi], 10, 100][[1]] (* G. C. Greubel, Mar 27 2018 *)

Prog

(PARI) -zeta(1/2)/sqrt(2*Pi) \\ Charles R Greathouse IV, Mar 10 2016

Crossrefs

Cf. A134470 (continued fraction), A134471 (Numerators of continued fraction convergents), A134472 (Denominators of continued fraction convergents).

Sequence in context: A256453 A276627 A119420 * A238166 A227417 A260061

Adjacent sequences: A134466 A134467 A134468 * A134470 A134471 A134472

Keyword

cons,nonn

Author

Hans J. H. Tuenter, Oct 27 2007

Extensions

More decimals from Vaclav Kotesovec, Mar 21 2016

Status

approved