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A249022
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Decimal expansion of Sine Euler constant.
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2
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4, 6, 6, 5, 9, 9, 3, 0, 6, 2, 0, 3, 7, 2, 9, 2, 6, 5, 2, 2, 1, 7, 3, 4, 2, 2, 0
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OFFSET
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0,1
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COMMENTS
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The Sine Euler constant is introduced here as the limit as n increases without bound of sum{sin(1/k), k = 1..n} - integral{sin(1/x) over [1,n]}; this is analogous to the Euler constant, defined as the limit of sum{1/k, k = 1..n} - integral{1/x over [1,n]}.
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LINKS
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EXAMPLE
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Sine Euler constant = 0.466599306203729265221734220...
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MATHEMATICA
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f = DifferenceRoot[Function[{\[FormalY], \[FormalN]}, {((2 \[FormalN] - z) (2 \[FormalN] - (z + 1))) \[FormalY][\[FormalN]] + \[FormalY][1 + \[FormalN]] == 0, \[FormalY][1] == -1}]];
(Total[Table[1/((-1)^(n + 1) (2 n - 1)!) HarmonicNumber[k, 2 n - 1], {n, 50}]] /. k -> #) - (CosIntegral[1] - CosIntegral[1/#] - Sin[1] + # Sin[1/#]) &[N[10^35, 40]]
RealDigits[t][[1]]
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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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