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%I A259068 #18 Mar 19 2024 06:52:22
%S A259068 0,0,5,3,7,8,5,7,6,3,5,7,7,7,4,3,0,1,1,4,4,4,1,6,9,7,4,2,1,0,4,1,3,8,
%T A259068 4,2,8,9,5,6,6,4,4,3,9,7,4,2,2,9,5,5,0,7,0,5,9,4,4,7,0,2,3,2,2,3,3,2,
%U A259068 4,5,0,1,9,9,7,9,2,4,0,6,9,5,8,6,0,9,5,1,0,3,8,7,0,8,2,5,6,8,3,2,6,7,1,2,2,4,3
%N A259068 Decimal expansion of zeta'(-3) (the derivative of Riemann's zeta function at -3).
%D A259068 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15.1 Generalized Glaisher constants, p. 136-137.
%H A259068 G. C. Greubel, <a href="/A259068/b259068.txt">Table of n, a(n) for n = 0..10000</a>
%H A259068 Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>.
%H A259068 Wikipedia, <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann Zeta Function</a>
%H A259068 <a href="/wiki/Index_to_constants#Start_of_section_Z">Index entries for constants related to zeta</a>
%F A259068 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 A259068 zeta'(-3) = -11/720 - log(A(3)), where A(3) is A243263.
%F A259068 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
%e A259068 0.0053785763577743011444169742104138428956644397422955070594470232233245...
%t A259068 Join[{0, 0}, RealDigits[Zeta'[-3], 10, 105] // First]
%Y A259068 Cf. A000335, A000391, A000417, A000428, A023872, A057527, A057528, A255050, A255052, A258350, A258351, A258352, A260404.
%K A259068 nonn,cons
%O A259068 0,3
%A A259068 _Jean-François Alcover_, Jun 18 2015

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