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A068982
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Decimal expansion of the limit of the product of a modified Zeta function.
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3
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4, 3, 5, 7, 5, 7, 0, 7, 6, 7, 7, 2, 6, 4, 5, 5, 9, 3, 7, 3, 7, 6, 2, 2, 9, 7, 0, 1, 2, 0, 9, 4, 1, 8, 6, 3, 4, 9, 6, 8, 6, 4, 1, 7, 4, 9, 2, 4, 3, 6, 8, 0, 3, 8, 1, 7, 5, 4, 6, 0, 9, 8, 9, 0, 9, 2, 3, 0, 0, 2, 3, 6, 0, 1, 6, 1, 0, 3, 0, 5, 3, 1, 8, 8, 0, 4, 3, 9, 7, 9, 5, 9, 7, 7, 2, 3, 4, 0, 6, 5, 3, 7, 6, 9
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OFFSET
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0,1
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COMMENTS
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The "modified Zeta function" Zetam(n) = sum(mu(k)/k^n) may be helpful when searching for a closed form for Apery's constant.
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LINKS
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FORMULA
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Equals Product_{k=1..oo} Sum_{n=2..oo} mu(k)/k^n.
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EXAMPLE
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0.43575707...
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MAPLE
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with(numtheory); evalf(Product(Sum('mobius(k)/k^n', 'k'=1..infinity), n=2..infinity), 40); Note: For practical reasons you should change "infinity" to some finite value.
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MATHEMATICA
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digits = 104; 1/NProduct[ Zeta[n], {n, 2, Infinity}, WorkingPrecision -> digits+10, NProductFactors -> 1000] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 15 2013 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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Andre Neumann Kauffman (andrekff(AT)hotmail.com), Apr 01 2002
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EXTENSIONS
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STATUS
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approved
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