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A210593
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Decimal expansion of the series limit of Sum_{k>=1} (-1)^k*log(k)/k^2.
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6
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1, 0, 1, 3, 1, 6, 5, 7, 8, 1, 6, 3, 5, 0, 4, 5, 0, 1, 8, 8, 6, 0, 0, 2, 8, 8, 2, 2, 1, 2, 2, 4, 2, 1, 8, 3, 6, 5, 9, 3, 8, 4, 7, 7, 6, 3, 7, 4, 9, 1, 1, 1, 6, 3, 3, 3, 4, 2, 9, 4, 2, 4, 7, 1, 9, 6, 2, 0, 4, 5, 3, 0, 9, 2, 0, 5, 4, 3, 6, 3, 2, 4, 9, 5, 3, 1, 7, 8, 0, 1, 2, 5, 3, 1, 9, 0, 3, 5, 6, 3, 9, 8, 2, 3, 1
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OFFSET
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0,4
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COMMENTS
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First derivative of the Dirichlet eta-function eta(s) at s=2.
Phatisena et al. misspell "Euler" and provide the wrong sign and an invalid 7th digit.
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LINKS
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FORMULA
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Decimal expansion of (log(2)*zeta(2) + zeta'(2)) / 2.
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EXAMPLE
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0.101316578163504501886002882212242183659384776374911163334294247196204...
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MAPLE
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1/2*log(2)*Zeta(2)+Zeta(1, 2)/2 ; evalf(%) ;
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MATHEMATICA
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N[(1/12)*Pi^2*(Log[4] - 12*Log[Glaisher] + Log[Pi] + EulerGamma), 105] // RealDigits // First (* Jean-François Alcover, Feb 05 2013 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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