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A259069
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Decimal expansion of zeta'(-4) (the derivative of Riemann's zeta function at -4).
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14
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0, 0, 7, 9, 8, 3, 8, 1, 1, 4, 5, 0, 2, 6, 8, 6, 2, 4, 2, 8, 0, 6, 9, 6, 6, 7, 0, 7, 9, 8, 7, 8, 9, 3, 0, 3, 9, 0, 5, 2, 3, 7, 6, 9, 3, 3, 6, 2, 2, 9, 8, 8, 7, 6, 4, 1, 7, 7, 0, 4, 7, 3, 9, 7, 1, 4, 0, 2, 8, 7, 4, 0, 2, 8, 1, 8, 7, 8, 6, 5, 7, 9, 5, 2, 5, 4, 3, 9, 6, 1, 9, 6, 9, 2, 8, 6, 9, 8, 2, 0, 3, 9, 6, 4, 4, 4
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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, pp. 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'(-4) = 3*zeta(5)/(4*Pi^4) = -log(A(4)), where A(4) is A243264.
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EXAMPLE
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0.00798381145026862428069667079878930390523769336229887641770473971402874...
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MATHEMATICA
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Join[{0, 0}, RealDigits[Zeta'[-4], 10, 104] // First]
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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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