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..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'(-3) = -11/720 - log(A(3)), where A(3) is A243263.
Equals -11/720 + (gamma + log(2*Pi))/120 - 3*Zeta'(4)/(4*Pi^4), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jul 24 2015
EXAMPLE
0.0053785763577743011444169742104138428956644397422955070594470232233245...
MATHEMATICA
Join[{0, 0}, RealDigits[Zeta'[-3], 10, 105] // First]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Jun 18 2015
STATUS
approved