OFFSET
0,4
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15.1 Generalized Glaisher constants, p. 136-137.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
Eric Weisstein's MathWorld, Riemann Zeta Function.
Wikipedia, Riemann Zeta Function
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
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Jun 18 2015
STATUS
approved