OFFSET
0,3
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..1500
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'(-6) = -45*zeta(7)/(8*Pi^6) = -log(A(6)).
EXAMPLE
-0.0058997591435159374506298774083920255798015346201571958652393922063597...
MATHEMATICA
Join[{0, 0}, RealDigits[Zeta'[-6], 10, 104] // First]
PROG
(PARI) zeta'(-6) \\ Altug Alkan, Dec 11 2015
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Jun 18 2015
STATUS
approved