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
J. B. Rosser, L. Schoenfeld, Approximate formulas for some functions of prime numbers, Ill. J. Math. 6 (1) (1962) 64-94, Table IV
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'(-5) = 137/15120 - log(A(5)), where A(5) is A243265.
Equals 137/15120 - (gamma + log(2*Pi))/252 + 15*Zeta'(6) / (4*Pi^6), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jul 25 2015
EXAMPLE
-0.000572985980198635204990994148833874513253987291199521217820791880997735...
MATHEMATICA
Join[{0, 0, 0}, RealDigits[Zeta'[-5], 10, 103] // First]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Jun 18 2015
STATUS
approved