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A324996
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Decimal expansion of zeta'(-1, 3/4) (negated).
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3
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0, 5, 2, 2, 1, 2, 5, 8, 3, 0, 4, 5, 1, 4, 8, 3, 2, 8, 8, 8, 2, 8, 5, 6, 1, 5, 6, 5, 8, 6, 7, 5, 1, 1, 4, 9, 3, 7, 0, 5, 1, 1, 9, 9, 0, 9, 5, 4, 5, 5, 9, 0, 9, 4, 6, 0, 6, 9, 3, 5, 1, 0, 3, 9, 8, 3, 2, 6, 6, 9, 4, 6, 7, 6, 1, 7, 8, 7, 5, 6, 8, 8, 3, 6, 7, 1, 6, 0, 6, 8, 5, 3, 4, 2, 1, 9, 9, 2, 0, 2, 8, 4, 9, 4, 6, 0
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OFFSET
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0,2
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LINKS
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FORMULA
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Equals Pi/32 - PolyGamma(1, 1/4)/(32*Pi) - Zeta'(-1)/8.
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EXAMPLE
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-0.05221258304514832888285615658675114937051199095455909460693510398326...
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MAPLE
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evalf(Zeta(1, -1, 3/4), 120);
evalf(Pi/32 - Psi(1, 1/4)/(32*Pi) - Zeta(1, -1)/8, 120);
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MATHEMATICA
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RealDigits[Derivative[1, 0][Zeta][-1, 3/4], 10, 120][[1]]
N[With[{k=1}, (4^k-1) * BernoulliB[2*k] * Pi/4^(k+1)/k + (4^(k-1) - 1) * BernoulliB[2*k] * Log[2]/k/2^(4*k-1) + (-1)^k*PolyGamma[2*k-1, 1/4] / 4 / (8*Pi)^(2*k-1) - (4^k-2)*Zeta'[1-2*k]/2^(4*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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