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A259072
Decimal expansion of zeta'(-7) (the derivative of Riemann's zeta function at -7) (negated).
17
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
OFFSET
0,4
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15.1 Generalized Glaisher constants, p. 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'(-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
EXAMPLE
-0.000728642680159240652467233354650360611902887720925418318636386154...
MATHEMATICA
Join[{0, 0, 0}, RealDigits[Zeta'[-7], 10, 104] // First]
PROG
(PARI) -zeta'(-7) \\ Charles R Greathouse IV, Dec 04 2016
CROSSREFS
Sequence in context: A249506 A199046 A198564 * A107311 A363538 A048836
KEYWORD
nonn,cons
AUTHOR
STATUS
approved