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A134469
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Decimal expansion of -zeta(1/2)/sqrt(2*Pi).
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4
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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
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0,1
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COMMENTS
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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.
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LINKS
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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.
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FORMULA
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-zeta(1/2)/sqrt(2*Pi)= A059750/A019727.
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EXAMPLE
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0.58259715793901067020517716418763115472909387019865...
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MAPLE
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Digits:=100; evalf(-Zeta(1/2)/sqrt(2*Pi));
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MATHEMATICA
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RealDigits[-Zeta[1/2]/Sqrt[2*Pi], 10, 100][[1]] (* G. C. Greubel, Mar 27 2018 *)
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PROG
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(PARI) -zeta(1/2)/sqrt(2*Pi) \\ Charles R Greathouse IV, Mar 10 2016
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CROSSREFS
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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
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KEYWORD
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cons,nonn
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AUTHOR
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Hans J. H. Tuenter, Oct 27 2007
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EXTENSIONS
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More decimals from Vaclav Kotesovec, Mar 21 2016
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STATUS
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approved
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