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A375368
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Decimal expansion of zeta'(2)/(2*Pi^2) + log(2*Pi)/6 - gamma/12.
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1
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2, 1, 0, 7, 1, 4, 7, 8, 9, 5, 6, 8, 5, 5, 2, 1, 0, 8, 3, 4, 2, 9, 1, 1, 8, 7, 4, 6, 2, 6, 6, 9, 4, 8, 4, 3, 8, 3, 3, 3, 2, 9, 0, 2, 3, 1, 5, 0, 3, 5, 6, 5, 8, 9, 4, 0, 8, 7, 2, 0, 1, 3, 0, 5, 5, 0, 6, 8, 9, 8, 1, 4, 9, 6, 3, 7, 1, 9, 6, 9, 2, 7, 5, 4, 5, 1, 3, 2, 1
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OFFSET
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0,1
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COMMENTS
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zeta'(2) = -0.9375.. is the first derivative of the zeta function (see A073002). Gamma is A001620.
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LINKS
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FORMULA
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Equals Integral_{x=0..1} x* log(Gamma(x)) dx.
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EXAMPLE
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0.21071478956855210834291187462669484383332902315035...
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MAPLE
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Zeta(1, 2)/2/Pi^2+log(2*Pi)/6-gamma/12 ; evalf(%) ;
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MATHEMATICA
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RealDigits[Zeta'[2] / (2*Pi^2) + Log[2*Pi] / 6 - EulerGamma / 12, 10, 120][[1]] (* Amiram Eldar, Aug 19 2024 *)
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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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