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A084448
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Decimal expansion of (negative of) Kinkelin constant.
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44
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1, 6, 5, 4, 2, 1, 1, 4, 3, 7, 0, 0, 4, 5, 0, 9, 2, 9, 2, 1, 3, 9, 1, 9, 6, 6, 0, 2, 4, 2, 7, 8, 0, 6, 4, 2, 7, 6, 4, 0, 3, 6, 3, 8, 0, 3, 3, 5, 2, 0, 1, 7, 8, 3, 6, 6, 6, 5, 2, 2, 3, 0, 6, 3, 5, 7, 3, 5, 9, 6, 9, 9, 6, 6, 6, 5, 7, 7, 1, 7, 2, 7, 5, 9, 5, 2, 5, 1, 0, 0, 3, 3, 2, 5, 0, 8, 7, 5, 5
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OFFSET
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0,2
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COMMENTS
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Named after the Swiss mathematician Hermann Kinkelin (1832-1913). - Amiram Eldar, Jun 16 2021
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LINKS
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FORMULA
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Zeta(1, -1). Almkvist gives many formulas.
Equals (1 - gamma - log(2*Pi))/12 + Zeta'(2)/(2*Pi^2), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jul 25 2015
Equals 1/24 - gamma/3 - Sum_{k>=1} (zeta(2*k+1)-1)/((2*k+1)*(2*k+3)) = 1/12 - log(A), where A is the Glaisher-Kinkelin constant (A074962) (Kinkelin, 1860).
Equals 2 * Integral_{x>=0} x*log(x)/(exp(2*Pi*x)-1) dx (Wright, 1931). (End)
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EXAMPLE
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-0.1654211437004509292139196602427806427640363803352017836665223...
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MAPLE
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Digits := 200; evalf(Zeta(1, -1));
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MATHEMATICA
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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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