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Search: id:A094721
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| A094721 |
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Fill's second logarithmic constant. |
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+0
2
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| 2, 0, 2, 5, 4, 3, 8, 4, 6, 7, 7, 7, 6, 5, 7, 3, 8, 8, 7, 7, 1, 3, 5, 1, 8, 7, 3, 9, 1, 4, 1, 7, 6, 5, 2, 4, 7, 0, 6, 5, 2, 9, 3, 0, 6, 1, 7, 6, 5, 8, 2, 8, 3, 9, 5, 5, 6, 2, 9, 2, 4, 7, 5, 5, 2, 6, 2, 3, 2, 4, 2, 5, 0, 9, 6, 3, 2, 5, 4, 7, 3, 7, 9, 1, 9, 3, 2, 2, 0, 8, 4, 1, 6, 5, 3, 8, 6, 5, 9, 6, 8, 6, 4, 7, 5
(list; cons; graph; listen)
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OFFSET
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1,1
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LINKS
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J. A. Fill, Ph. Flajolet and N. Kapur, Singularity analysis, Hadamard products, and tree recurrences
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FORMULA
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Sum[k>=1, log(k)/{(k+1)*4^k} * C(2n, n)].
-gamma-Integral_{0..1}, log(log(1/t))/{ sqrt(1-t)(1+sqrt(1-t))2 } dt. - Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 24 2004
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EXAMPLE
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2.0254384677765738877...
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MATHEMATICA
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$MaxExtraPrecision = 256; $MaxPrecision = 2560000; k = NIntegrate[ Log[ Log[1/t]]/(Sqrt[1 - t](1 + Sqrt[1 - t])^2), {t, 0, 1}, AccuracyGoal -> 80, WorkingPrecision -> 128, MaxRecursion -> 32]; RealDigits[ N[ -EulerGamma - k, 105]][[1]] (from Robert G. Wilson v Aug 24 2004)
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CROSSREFS
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Cf. A094720.
Sequence in context: A005074 A078182 A133394 this_sequence A011297 A110282 A024308
Adjacent sequences: A094718 A094719 A094720 this_sequence A094722 A094723 A094724
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KEYWORD
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nonn,cons
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AUTHOR
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Ralf Stephan, May 25 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 24 2004
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