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Search: id:A068982
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| A068982 |
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Limit of the product of a modified Zeta function. |
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+0
1
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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
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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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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FORMULA
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Product(Sum(mu(k)/k^n)), k=1..infinity, n=2..infinity
Equals 1/A021002. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 31 2009]
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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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CROSSREFS
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Cf. A021002, A002117.
Sequence in context: A023829 A000211 A059902 this_sequence A035427 A010475 A033546
Adjacent sequences: A068979 A068980 A068981 this_sequence A068983 A068984 A068985
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KEYWORD
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cons,nonn
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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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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 31 2009
Example corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 23 2009
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