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A263192
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Decimal expansion of Sum_{n >= 1} cos(n)/sqrt(n), negated.
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6
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1, 9, 4, 1, 0, 8, 9, 3, 5, 0, 9, 2, 1, 8, 2, 0, 4, 9, 7, 3, 9, 1, 4, 9, 2, 4, 4, 9, 2, 8, 1, 9, 4, 7, 2, 6, 6, 3, 5, 3, 2, 0, 5, 5, 2, 6, 3, 4, 0, 4, 7, 8, 1, 5, 4, 0, 2, 3, 9, 8, 3, 7, 6, 6, 0, 9, 5, 6, 6, 6, 8, 3, 7, 2, 6, 2, 5, 5, 4, 7, 6, 4, 0, 0, 6, 5, 3, 1, 8, 9, 6, 4, 9, 6, 5, 5, 2, 4, 7, 0, 1, 2, 2, 6, 8, 3, 5, 1, 9
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OFFSET
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0,2
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COMMENTS
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A slowly convergent series. It may be efficiently computed via the Hurwitz zeta-function (see formula below).
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LINKS
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FORMULA
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(Zeta(1/2, 1/(2*Pi)) + Zeta(1/2, 1-1/(2*Pi)))/2, see formula (26) in the reference.
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EXAMPLE
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-0.1941089350921820497391492449281947266353205526340478...
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MAPLE
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evalf(1/2*(Zeta(0, 1/2, 1/(2*Pi)) + Zeta(0, 1/2, 1-1/(2*Pi))), 120);
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MATHEMATICA
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N[(Zeta[1/2, 1/(2*Pi)] + Zeta[1/2, 1 - 1/(2*Pi)])/2, 200]
RealDigits[Re[(1/2)*(PolyLog[1/2, E^(-I)] + PolyLog[1/2, E^I])], 10, 109][[1]] (* Vaclav Kotesovec, Oct 31 2015 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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