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A256922
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Decimal expansion of Sum_{k>=2} (-1)^k*zeta(k)/(k*2^k).
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2
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1, 6, 7, 8, 2, 5, 5, 9, 4, 8, 1, 5, 5, 2, 1, 2, 0, 7, 9, 5, 7, 7, 3, 7, 5, 9, 9, 2, 5, 9, 5, 5, 4, 0, 0, 3, 2, 6, 9, 2, 2, 6, 9, 4, 0, 0, 6, 7, 3, 6, 2, 3, 3, 1, 0, 3, 9, 0, 1, 5, 1, 4, 3, 6, 8, 5, 1, 0, 9, 1, 2, 6, 3, 6, 1, 5, 5, 0, 6, 5, 9, 7, 5, 4, 4, 2, 1, 8, 3, 9, 7, 8, 7, 1, 9, 9, 5, 4, 1, 0, 6, 6, 3, 1, 9
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OFFSET
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0,2
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REFERENCES
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H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights (2011) p. 272.
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LINKS
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FORMULA
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Equals A001620/2 + (1/2)*log(Pi) - log(2).
Equals Sum_{k>=1} (1/(2*k) - log(1 + 1/(2*k))). - Amiram Eldar, Jul 22 2020
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EXAMPLE
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0.167825594815521207957737599259554003269226940067362331039...
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MATHEMATICA
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RealDigits[EulerGamma/2 + (1/2)*Log[Pi] - Log[2], 10, 105] // First
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PROG
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(PARI) Euler/2 + log(Pi)/2 - log(2) \\ Michel Marcus, Apr 13 2015
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/2 + (1/2)*Log(Pi(R)) - Log(2); // G. C. Greubel, Sep 05 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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