A349252 - OEIS

A349252

Decimal expansion of Sum_{k>=1} (-1)^k * log(k) / k^4.

%I #11 Nov 13 2021 05:55:35

%S 0,3,3,4,7,8,8,0,4,5,7,8,5,6,5,0,6,6,3,8,5,9,5,6,8,5,4,7,8,8,7,3,7,7,

%T 9,9,7,1,3,7,5,9,7,3,0,4,0,5,7,3,4,9,7,4,8,2,8,6,6,5,7,6,4,2,8,8,6,8,

%U 3,6,2,2,5,2,7,9,5,8,8,3,8,1,0,7,9,5,3,4,7,4,7,5,8,6,5,8,6,4,8,6,2,2,8,2,6,6,5,1,1,1,1,2,1,8,5,5,1,7,9,8,3

%N Decimal expansion of Sum_{k>=1} (-1)^k * log(k) / k^4.

%C First derivative of the Dirichlet eta function at 4.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DirichletEtaFunction.html">Dirichlet Eta Function</a>

%F Equals (Pi^4 * log(2) + 630 * zeta'(4)) / 720.

%e 0.0334788045785650663859568547887377997137597304057...

%t Flatten[{0, RealDigits[(Pi^4 Log[2] + 630 Zeta'[4])/720, 10, 120][[1]]}]

%o (PARI) sumalt(k=1, (-1)^k * log(k) / k^4) \\ _Michel Marcus_, Nov 12 2021

%Y Cf. A013662, A091812, A210593, A256358, A261506, A267315, A349220.

%K nonn,cons

%O 0,2

%A _Ilya Gutkovskiy_, Nov 12 2021