

A134469


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


4



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
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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) 787802.
Alain Comtet and Satya N. Majumdar, Precise Asymptotics for a Random Walkerâ€™s Maximum, J. Stat. Mech. Theor. Exp. 06 (2005) P06013, arXiv:condmat/0506195 [condmat.statmech], 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) 481488.
Robert A. Wijsman, Overshoot in the Case of Normal Variables, Sequential Analysis, 23(2):275284, 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



