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

Author

Hans J. H. Tuenter, Oct 27 2007

Keywords

• cons
• nonn

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.

Examples

			0.58259715793901067020517716418763115472909387019865...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 5.9, p. 326.

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.

Crossrefs

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

Programs

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 *)

PARI

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

Formula

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

Extensions

More decimals from Vaclav Kotesovec, Mar 21 2016