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A324994
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Decimal expansion of zeta'(-1, 2/3) (negated).
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2
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0, 1, 3, 9, 6, 2, 4, 4, 7, 3, 1, 2, 3, 7, 0, 7, 4, 3, 8, 8, 0, 3, 4, 4, 6, 0, 4, 4, 4, 1, 4, 0, 9, 2, 6, 3, 9, 8, 8, 5, 7, 6, 6, 5, 9, 9, 8, 8, 1, 2, 4, 3, 1, 7, 1, 8, 4, 8, 4, 1, 3, 9, 7, 5, 7, 4, 9, 0, 3, 3, 7, 2, 9, 8, 4, 8, 3, 3, 2, 6, 2, 8, 5, 6, 2, 5, 6, 4, 5, 3, 5, 5, 4, 2, 4, 9, 7, 0, 3, 6, 2, 1, 5, 1, 0, 6
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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 Pi/(18*sqrt(3)) - log(3)/72 - PolyGamma(1, 1/3) / (12*sqrt(3)*Pi) - Zeta'(-1)/3.
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EXAMPLE
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-0.01396244731237074388034460444140926398857665998812431718484139757490...
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MAPLE
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evalf(Zeta(1, -1, 2/3), 120);
evalf(Pi/(18*sqrt(3)) - log(3)/72 - Psi(1, 1/3) / (12*sqrt(3)*Pi) - Zeta(1, -1)/3, 120);
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MATHEMATICA
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RealDigits[Derivative[1, 0][Zeta][-1, 2/3], 10, 120][[1]]
N[With[{k=1}, Sqrt[3] * (9^k - 1) * BernoulliB[2*k] * Pi / (9^k * 8*k) - 3*BernoulliB[2*k] * Log[3] / 9^k / 4 / k + (-1)^k * PolyGamma[2*k-1, 1/3] / 2 / Sqrt[3] / (6*Pi)^(2*k-1) - (9^k-3)*Zeta'[-2*k+1]/2/9^k], 120]
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PROG
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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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