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A259073 Decimal expansion of zeta'(-8) (the derivative of Riemann's zeta function at -8).

%I A259073 #15 Feb 16 2025 08:33:25
%S A259073 0,0,8,3,1,6,1,6,1,9,8,5,6,0,2,2,4,7,3,5,9,5,2,4,4,2,6,5,1,0,5,3,4,2,
%T A259073 1,4,2,2,5,6,7,4,1,2,2,9,1,8,8,2,9,9,9,9,0,4,0,2,1,0,5,3,2,7,5,3,0,5,
%U A259073 6,9,1,7,4,0,7,8,8,1,2,3,5,3,8,3,4,8,3,4,5,2,5,1,4,5,2,4,4,0,3,5,1,7,4,1,2,6
%N A259073 Decimal expansion of zeta'(-8) (the derivative of Riemann's zeta function at -8).
%D A259073 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15.1 Generalized Glaisher constants, p. 136-137.
%H A259073 G. C. Greubel, <a href="/A259073/b259073.txt">Table of n, a(n) for n = 0..2000</a>
%H A259073 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>.
%H A259073 Wikipedia, <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann Zeta Function</a>
%H A259073 <a href="/wiki/Index_to_constants#Start_of_section_Z">Index entries for constants related to zeta</a>
%F A259073 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 A259073 zeta'(-8) = 315*zeta(9)/(4*Pi^8) = -log(A(8)).
%e A259073 0.0083161619856022473595244265105342142256741229188299990402105327530569174...
%t A259073 Join[{0, 0}, RealDigits[Zeta'[-8], 10, 104] // First]
%o A259073 (PARI) zeta'(-8) \\ _Altug Alkan_, Dec 08 2015
%K A259073 nonn,cons
%O A259073 0,3
%A A259073 _Jean-François Alcover_, Jun 18 2015