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%I #11 Jul 16 2021 11:24:47
%S 0,0,3,1,3,0,1,4,5,3,1,9,7,8,8,5,7,2,7,5,4,9,2,5,7,6,8,2,9,0,7,8,5,4,
%T 4,6,7,0,2,6,6,9,3,6,5,8,6,5,4,8,1,5,1,5,9,6,4,9,0,5,1,3,3,2,0,5,4,3,
%U 4,7,1,6,3,0,1,4,2,9,6,4,3,4,9,4,3,0,9,5,1
%N Decimal expansion of zeta'(-9) (the derivative of Riemann's zeta function at -9).
%H G. C. Greubel, <a href="/A266260/b266260.txt">Table of n, a(n) for n = 0..1501</a>
%F zeta'(-n) = HarmonicNumber(n)*BernoulliB(n+1)/(n+1) - log(A(n)), where A(n) is the n-th Bendersky constant.
%F zeta'(-9) = 7129/332640 - log(A(9)).
%e 0.0031301453197885727549257682907854467026693658654815.....
%t Join[{0, 0}, RealDigits[Zeta'[-9], 10, 100] // First]
%t N[Zeta'[-9], 100]
%Y Cf. A075700 (zeta'(0)), A084448 (zeta'(-1)), A240966 (zeta'(-2)), A259068 (zeta'(-3)), A259069 (zeta'(-4)), A259070 (zeta'(-5)), A259071 (zeta'(-6)), A259072 (zeta'(-7)), A259073 (zeta'(-8)), A266261 (zeta'(-10)), A266262 (zeta'(-11)), A266263 (zeta'(-12)), A260660 (zeta'(-13)), A266264 (zeta'(-14)), A266270 (zeta'(-15)), A266271 (zeta'(-16)), A266272 (zeta'(-17)), A266273 (zeta'(-18)), A266274 (zeta'(-19)), A266275 (zeta'(-20)).
%K nonn,cons,easy
%O 0,3
%A _G. C. Greubel_, Dec 25 2015
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