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A259072
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Decimal expansion of zeta'(-7) (the derivative of Riemann's zeta function at -7) (negated).
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17
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0, 0, 0, 7, 2, 8, 6, 4, 2, 6, 8, 0, 1, 5, 9, 2, 4, 0, 6, 5, 2, 4, 6, 7, 2, 3, 3, 3, 5, 4, 6, 5, 0, 3, 6, 0, 6, 1, 1, 9, 0, 2, 8, 8, 7, 7, 2, 0, 9, 2, 5, 4, 1, 8, 3, 1, 8, 6, 3, 6, 3, 8, 6, 1, 5, 4, 1, 4, 2, 5, 9, 7, 5, 4, 5, 5, 2, 7, 3, 0, 9, 9, 1, 3, 0, 2, 3, 2, 4, 6, 4, 4, 1, 6, 8, 0, 4, 4, 9, 3, 7, 9, 6, 0, 6, 5, 4
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OFFSET
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0,4
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15.1 Generalized Glaisher constants, p. 136-137.
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LINKS
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FORMULA
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zeta'(-n) = (BernoulliB(n+1)*HarmonicNumber(n))/(n+1) - log(A(n)), where A(n) is the n-th Bendersky constant, that is the n-th generalized Glaisher constant.
zeta'(-7) = -121/11200 - log(A(7)).
Equals -121/11200 + (gamma + log(2*Pi))/240 - 315*Zeta'(8)/(8*Pi^8), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jul 25 2015
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EXAMPLE
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-0.000728642680159240652467233354650360611902887720925418318636386154...
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MATHEMATICA
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Join[{0, 0, 0}, RealDigits[Zeta'[-7], 10, 104] // First]
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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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