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%I #38 Jul 16 2021 07:21:19
%S 0,6,3,7,4,9,8,7,3,7,4,4,5,7,6,8,8,0,2,8,6,0,3,8,6,8,1,4,7,3,3,3,5,0,
%T 5,5,6,4,8,8,2,7,3,5,5,3,1,2,7,5,8,4,9,1,3,8,5,1,0,0,8,8,5,8,8,7,7,3,
%U 7,0,6,4,2,0,1,5,6,6,6,8,7,0,9,4,7,0,9,2,6,7,8,1,5,3,5,8,2,6,3,1,8,7,8,2,4,3,7
%N Decimal expansion of zeta'(-13) (the derivative of Riemann's zeta function at -13).
%H G. C. Greubel, <a href="/A260660/b260660.txt">Table of n, a(n) for n = 0..1500</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'(-13) = (1145993/4324320) - log(A(13)).
%F zeta'(-13) = 1145993/4324320 - gamma/12 - log(2*Pi)/12 + 6081075*Zeta'(14) / (8*Pi^14), where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Dec 05 2015
%e 0.06374987374457688028603868147333505564882735...
%t N[Zeta'[-13]]
%t Join[{0}, RealDigits[Zeta'[-13], 10, 1500] // First]
%o (PARI) zeta'(-13) \\ _Altug Alkan_, Nov 13 2015
%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)), A266260 (zeta'(-9)), A266261 (zeta'(-10)), A266262 (zeta'(-11)), A266263 (zeta'(-12)), A266264 (zeta'(-14)), A266270 (zeta'(-15)), A266271 (zeta'(-16)), A266272 (zeta'(-17)), A266273 (zeta'(-18)), A266274 (zeta'(-19)), A266275 (zeta'(-20)).
%K nonn,cons
%O 0,2
%A _G. C. Greubel_, Nov 13 2015
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