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A259071 Decimal expansion of zeta'(-6) (the derivative of Riemann's zeta function at -6) (negated).

%I A259071 #14 Feb 16 2025 08:33:25
%S A259071 0,0,5,8,9,9,7,5,9,1,4,3,5,1,5,9,3,7,4,5,0,6,2,9,8,7,7,4,0,8,3,9,2,0,
%T A259071 2,5,5,7,9,8,0,1,5,3,4,6,2,0,1,5,7,1,9,5,8,6,5,2,3,9,3,9,2,2,0,6,3,5,
%U A259071 9,7,0,3,7,5,9,4,2,4,9,0,5,7,2,3,0,2,3,8,6,3,0,0,7,5,4,2,2,5,8,3,8,5,3,6,4,8
%N A259071 Decimal expansion of zeta'(-6) (the derivative of Riemann's zeta function at -6) (negated).
%D A259071 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15.1 Generalized Glaisher constants, p. 136-137.
%H A259071 G. C. Greubel, <a href="/A259071/b259071.txt">Table of n, a(n) for n = 0..1500</a>
%H A259071 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>.
%H A259071 Wikipedia, <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann Zeta Function</a>
%H A259071 <a href="/wiki/Index_to_constants#Start_of_section_Z">Index entries for constants related to zeta</a>
%F A259071 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 A259071 zeta'(-6) = -45*zeta(7)/(8*Pi^6) = -log(A(6)).
%e A259071 -0.0058997591435159374506298774083920255798015346201571958652393922063597...
%t A259071 Join[{0, 0}, RealDigits[Zeta'[-6], 10, 104] // First]
%o A259071 (PARI) zeta'(-6) \\ _Altug Alkan_, Dec 11 2015
%K A259071 nonn,cons
%O A259071 0,3
%A A259071 _Jean-François Alcover_, Jun 18 2015