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A306016
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Decimal expansion of -Zeta'(2)/Zeta(2).
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31
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5, 6, 9, 9, 6, 0, 9, 9, 3, 0, 9, 4, 5, 3, 2, 8, 0, 6, 3, 9, 9, 8, 6, 4, 3, 6, 0, 0, 1, 9, 7, 3, 0, 0, 0, 2, 4, 0, 3, 4, 8, 2, 2, 8, 0, 8, 0, 6, 9, 3, 0, 9, 7, 9, 5, 5, 8, 1, 9, 7, 3, 6, 0, 4, 3, 7, 9, 1, 7, 2, 7, 7, 3, 6, 6, 7, 4, 0, 6, 0, 6, 7, 8, 7, 8, 6, 7
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OFFSET
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0,1
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LINKS
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Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 179.
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FORMULA
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Equals -(6/Pi^2)*Zeta'(2).
Equals 1 - 12*Zeta'(-1) - gamma - log(2*Pi).
Equals Sum_{k>=1} Lambda(k)/k^2, where Lambda is the Mangoldt function.
Equals Sum_{p prime} log(p)/(p^2 - 1). (End)
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EXAMPLE
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Equals 0.569960993094532806399864360019730002403482280806930979558...
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MAPLE
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-(6/Pi^2)*Zeta(1, 2): evalf(%, 100);
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MATHEMATICA
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RealDigits[- Zeta'[2] / Zeta[2], 10, 87][[1]]
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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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