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A256784
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Decimal expansion of the generalized Euler constant gamma(5,12) (negated).
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15
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0, 0, 3, 3, 7, 2, 9, 4, 9, 3, 2, 2, 4, 0, 3, 2, 9, 7, 0, 2, 5, 0, 3, 2, 4, 9, 4, 8, 1, 8, 5, 9, 2, 1, 9, 4, 6, 1, 6, 0, 3, 4, 0, 3, 4, 6, 9, 9, 4, 9, 8, 3, 9, 5, 3, 8, 7, 3, 1, 6, 7, 0, 0, 8, 6, 3, 1, 2, 7, 1, 0, 3, 1, 6, 7, 6, 1, 5, 8, 5, 1, 3, 3, 3, 6, 5, 9, 1, 2, 3, 6, 3, 9, 7, 0, 0, 3, 1, 1, 9, 9, 9, 7, 7, 8, 7, 9
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OFFSET
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0,3
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LINKS
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FORMULA
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Equals EulerGamma/12 + 1/24*(Pi*(2-sqrt(3)) + 2*(sqrt(3)+1)*log(2) + log(3) - 4*sqrt(3) * log(sqrt(3)+1)).
Equals -(psi(5/12) + log(12))/12. - Amiram Eldar, Jan 07 2024
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EXAMPLE
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-0.0033729493224032970250324948185921946160340346994983953873167...
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MATHEMATICA
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Join[{0, 0}, RealDigits[-Log[12]/12 - PolyGamma[5/12]/12, 10, 105] // First]
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PROG
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(PARI) default(realprecision, 100); Euler/12 + 1/24*(Pi*(2-sqrt(3)) + 2*(sqrt(3)+1)*log(2) + log(3) - 4*sqrt(3)*log(sqrt(3)+1)) \\ G. C. Greubel, Aug 27 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/12 + 1/24*(Pi(R)*(2-Sqrt(3)) + 2*(Sqrt(3)+1)*Log(2) + Log(3) - 4*Sqrt(3)*Log(Sqrt(3)+1)); // G. C. Greubel, Aug 27 2018
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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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