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A259069
Decimal expansion of zeta'(-4) (the derivative of Riemann's zeta function at -4).
14
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
OFFSET
0,3
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15.1 Generalized Glaisher constants, pp. 136-137.
FORMULA
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.
EXAMPLE
0.00798381145026862428069667079878930390523769336229887641770473971402874...
MATHEMATICA
Join[{0, 0}, RealDigits[Zeta'[-4], 10, 104] // First]
CROSSREFS
Sequence in context: A372253 A256924 A348668 * A209328 A228049 A154943
KEYWORD
nonn,cons
AUTHOR
STATUS
approved