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A061444
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Decimal expansion of log(2 * Pi).
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15
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1, 8, 3, 7, 8, 7, 7, 0, 6, 6, 4, 0, 9, 3, 4, 5, 4, 8, 3, 5, 6, 0, 6, 5, 9, 4, 7, 2, 8, 1, 1, 2, 3, 5, 2, 7, 9, 7, 2, 2, 7, 9, 4, 9, 4, 7, 2, 7, 5, 5, 6, 6, 8, 2, 5, 6, 3, 4, 3, 0, 3, 0, 8, 0, 9, 6, 5, 5, 3, 1, 3, 9, 1, 8, 5, 4, 5, 2, 0, 7, 9, 5, 3, 8, 9, 4, 8, 6, 5, 9, 7, 2, 7, 1, 9, 0, 8, 3, 9, 5, 2, 4
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OFFSET
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1,2
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COMMENTS
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Used in formulas for gamma(x), e.g., in Stirling's approximation for m!.
Also decimal expansion of zeta'(0)/zeta(0). - Benoit Cloitre, Sep 28 2002
The value of log(2*Pi) is close to 1 + Sum_{n>=2} log(zeta(n)) = 1.83067035427178011248.... - Arkadiusz Wesolowski, Jul 17 2011
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LINKS
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FORMULA
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Equals 1 + Sum_{k>=1} zeta(2*k)/(k*(2*k + 1)). - Amiram Eldar, Aug 20 2020
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EXAMPLE
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1.837877066409345483560659472811235279722794947275566825634303...
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MATHEMATICA
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PROG
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(PARI) { default(realprecision, 20080); x=log(2*Pi); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b061444.txt", n, " ", d)) } \\ Harry J. Smith, Jul 22 2009
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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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