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Search: id:A118817
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| A118817 |
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Decimal expansion of Product_{n >= 1} cos(1/n). |
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+0
1
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| 3, 8, 8, 5, 3, 6, 1, 5, 3, 3, 3, 5, 1, 7, 5, 8, 5, 9, 1, 8, 4, 3, 2, 9, 5, 7, 5, 6, 8, 7, 0, 3, 5, 9, 0, 5, 0, 1, 3, 9, 0, 0, 5, 2, 8, 5, 9, 7, 5, 1, 7, 9, 2, 1, 9, 1, 3, 1, 8, 4, 6, 1, 1, 9, 9, 8, 7, 9
(list; cons; graph; listen)
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OFFSET
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1,1
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FORMULA
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a = prod(n=1..inf, cos(1/n)) a = exp(sum(n=1..inf, -c(n)*zeta(2n))), where c(n) = A046990(n)/A046991(n)
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EXAMPLE
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a = 0.388536153335175859...
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MATHEMATICA
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S = Series[Log[Cos[x]], {x, 0, 400}]; N[Exp[N[Sum[SeriesCoefficient[S, 2k] Zeta[2k], {k, 1, 200}], 70]], 50]
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CROSSREFS
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Cf. A046990, A046991.
Sequence in context: A101749 A019744 A102639 this_sequence A157471 A131596 A140975
Adjacent sequences: A118814 A118815 A118816 this_sequence A118818 A118819 A118820
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KEYWORD
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cons,nonn
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AUTHOR
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Fredrik Johansson (fredrik.johansson(AT)gmail.com), May 23 2006
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