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A259072 Decimal expansion of zeta'(-7) (the derivative of Riemann's zeta function at -7) (negated).

%I A259072 #15 Feb 16 2025 08:33:25
%S A259072 0,0,0,7,2,8,6,4,2,6,8,0,1,5,9,2,4,0,6,5,2,4,6,7,2,3,3,3,5,4,6,5,0,3,
%T A259072 6,0,6,1,1,9,0,2,8,8,7,7,2,0,9,2,5,4,1,8,3,1,8,6,3,6,3,8,6,1,5,4,1,4,
%U A259072 2,5,9,7,5,4,5,5,2,7,3,0,9,9,1,3,0,2,3,2,4,6,4,4,1,6,8,0,4,4,9,3,7,9,6,0,6,5,4
%N A259072 Decimal expansion of zeta'(-7) (the derivative of Riemann's zeta function at -7) (negated).
%D A259072 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15.1 Generalized Glaisher constants, p. 136-137.
%H A259072 G. C. Greubel, <a href="/A259072/b259072.txt">Table of n, a(n) for n = 0..10000</a>
%H A259072 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>.
%H A259072 Wikipedia, <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann Zeta Function</a>
%H A259072 <a href="/wiki/Index_to_constants#Start_of_section_Z">Index entries for constants related to zeta</a>
%F A259072 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 A259072 zeta'(-7) =  -121/11200 - log(A(7)).
%F A259072 Equals -121/11200 + (gamma + log(2*Pi))/240 - 315*Zeta'(8)/(8*Pi^8), where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Jul 25 2015
%e A259072 -0.000728642680159240652467233354650360611902887720925418318636386154...
%t A259072 Join[{0, 0, 0}, RealDigits[Zeta'[-7], 10, 104] // First]
%o A259072 (PARI) -zeta'(-7) \\ _Charles R Greathouse IV_, Dec 04 2016
%K A259072 nonn,cons
%O A259072 0,4
%A A259072 _Jean-François Alcover_, Jun 18 2015