A349252 Decimal expansion of Sum_{k>=1} (-1)^k * log(k) / k^4.

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, 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, 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

Offset: 0

Author

Ilya Gutkovskiy, Nov 12 2021

Keywords

• nonn
• cons

Comments

First derivative of the Dirichlet eta function at 4.

Examples

			0.0334788045785650663859568547887377997137597304057...
		

Links

• Eric Weisstein's World of Mathematics, Dirichlet Eta Function

Crossrefs

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

Programs

Mathematica

Flatten[{0, RealDigits[(Pi^4 Log[2] + 630 Zeta'[4])/720, 10, 120][[1]]}]

PARI

sumalt(k=1, (-1)^k * log(k) / k^4) \\ Michel Marcus, Nov 12 2021

Formula

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