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A259071
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Decimal expansion of zeta'(-6) (the derivative of Riemann's zeta function at -6) (negated).
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16
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0, 0, 5, 8, 9, 9, 7, 5, 9, 1, 4, 3, 5, 1, 5, 9, 3, 7, 4, 5, 0, 6, 2, 9, 8, 7, 7, 4, 0, 8, 3, 9, 2, 0, 2, 5, 5, 7, 9, 8, 0, 1, 5, 3, 4, 6, 2, 0, 1, 5, 7, 1, 9, 5, 8, 6, 5, 2, 3, 9, 3, 9, 2, 2, 0, 6, 3, 5, 9, 7, 0, 3, 7, 5, 9, 4, 2, 4, 9, 0, 5, 7, 2, 3, 0, 2, 3, 8, 6, 3, 0, 0, 7, 5, 4, 2, 2, 5, 8, 3, 8, 5, 3, 6, 4, 8
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OFFSET
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0,3
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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'(-6) = -45*zeta(7)/(8*Pi^6) = -log(A(6)).
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EXAMPLE
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-0.0058997591435159374506298774083920255798015346201571958652393922063597...
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MATHEMATICA
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Join[{0, 0}, RealDigits[Zeta'[-6], 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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