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A259069 Decimal expansion of zeta'(-4) (the derivative of Riemann's zeta function at -4).

%I A259069 #15 Feb 16 2025 08:33:25
%S A259069 0,0,7,9,8,3,8,1,1,4,5,0,2,6,8,6,2,4,2,8,0,6,9,6,6,7,0,7,9,8,7,8,9,3,
%T A259069 0,3,9,0,5,2,3,7,6,9,3,3,6,2,2,9,8,8,7,6,4,1,7,7,0,4,7,3,9,7,1,4,0,2,
%U A259069 8,7,4,0,2,8,1,8,7,8,6,5,7,9,5,2,5,4,3,9,6,1,9,6,9,2,8,6,9,8,2,0,3,9,6,4,4,4
%N A259069 Decimal expansion of zeta'(-4) (the derivative of Riemann's zeta function at -4).
%D A259069 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15.1 Generalized Glaisher constants, pp. 136-137.
%H A259069 G. C. Greubel, <a href="/A259069/b259069.txt">Table of n, a(n) for n = 0..1500</a>
%H A259069 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>.
%H A259069 Wikipedia, <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann Zeta Function</a>
%H A259069 <a href="/wiki/Index_to_constants#Start_of_section_Z">Index entries for constants related to zeta</a>
%F A259069 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.
%F A259069 zeta'(-4) = 3*zeta(5)/(4*Pi^4) = -log(A(4)), where A(4) is A243264.
%e A259069 0.00798381145026862428069667079878930390523769336229887641770473971402874...
%t A259069 Join[{0, 0}, RealDigits[Zeta'[-4], 10, 104] // First]
%K A259069 nonn,cons
%O A259069 0,3
%A A259069 _Jean-François Alcover_, Jun 18 2015