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Decimal expansion of zeta'(-8) (the derivative of Riemann's zeta function at -8).
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%I #14 Mar 19 2024 07:19:13

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

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15.1 Generalized Glaisher constants, p. 136-137.

%H G. C. Greubel, <a href="/A259073/b259073.txt">Table of n, a(n) for n = 0..2000</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann Zeta Function</a>

%H <a href="/wiki/Index_to_constants#Start_of_section_Z">Index entries for constants related to zeta</a>

%F 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 zeta'(-8) = 315*zeta(9)/(4*Pi^8) = -log(A(8)).

%e 0.0083161619856022473595244265105342142256741229188299990402105327530569174...

%t Join[{0, 0}, RealDigits[Zeta'[-8], 10, 104] // First]

%o (PARI) zeta'(-8) \\ _Altug Alkan_, Dec 08 2015

%K nonn,cons

%O 0,3

%A _Jean-François Alcover_, Jun 18 2015