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%I #7 Nov 11 2021 16:59:26
%S 0,5,9,7,0,5,9,0,6,1,6,0,1,9,5,3,5,8,3,6,3,4,2,9,2,6,6,2,8,7,9,2,5,6,
%T 7,8,3,1,6,9,2,6,8,7,3,1,5,6,5,1,5,9,6,9,2,3,3,2,5,1,1,7,8,0,5,2,4,0,
%U 1,0,0,5,6,0,1,1,6,2,2,8,0,2,3,4,6,3,7,0,2,4,9,7,1,6,9,2,8,9,5,1,8,7,0,8,3,1,8,1,9,6,7,0,1,0,8,2,1,6,1,1,2
%N Decimal expansion of Sum_{k>=1} (-1)^k * log(k) / k^3.
%C First derivative of the Dirichlet eta function at 3.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DirichletEtaFunction.html">Dirichlet Eta Function</a>
%F Equals (log(2) * zeta(3) + 3 * zeta'(3)) / 4.
%e 0.0597059061601953583634292662879256783169268731565...
%t Flatten[{0, RealDigits[(Log[2] Zeta[3] + 3 Zeta'[3])/4, 10, 120][[1]]}]
%o (PARI) sumalt(k=1, (-1)^k * log(k) / k^3) \\ _Michel Marcus_, Nov 11 2021
%Y Cf. A002117, A091812, A197070, A210593, A244115, A256358.
%K nonn,cons
%O 0,2
%A _Ilya Gutkovskiy_, Nov 11 2021
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