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Search: id:A134469
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| A134469 |
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Decimal expansion of -zeta(1/2)/sqrt(2*pi). |
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+0
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
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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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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REFERENCES
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Joseph T. Chang and Yuval Peres, "Ladder heights, Gaussian random walks and the Riemann zeta function", Annals of Probability, 25(2):787-802, 1997.
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):481-488, 2007.
Robert A. Wijsman, "Overshoot in the Case of Normal Variables", Sequential Analysis, 23(2):275-284, 2004.
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LINKS
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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):481-488, 2007.
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FORMULA
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-zeta(1/2)/sqrt(2*pi)
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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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CROSSREFS
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Cf. A134470 (continued fraction), A134471 (Numerators of continued fraction convergents), A134472 (Denominators of continued fraction convergents).
Sequence in context: A110989 A099736 A119420 this_sequence A010489 A099872 A097908
Adjacent sequences: A134466 A134467 A134468 this_sequence 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 (htuenter(AT)gmail.com), Oct 27 2007
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