A349220 Decimal expansion of Sum_{k>=1} (-1)^k * log(k) / k^3.

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, 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, 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

Offset: 0

Author

Ilya Gutkovskiy, Nov 11 2021

Keywords

• nonn
• cons

Comments

First derivative of the Dirichlet eta function at 3.

Examples

			0.0597059061601953583634292662879256783169268731565...
		

Links

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

Crossrefs

Cf. A002117, A091812, A197070, A210593, A244115, A256358.

Programs

Mathematica

Flatten[{0, RealDigits[(Log[2] Zeta[3] + 3 Zeta'[3])/4, 10, 120][[1]]}]

PARI

sumalt(k=1, (-1)^k * log(k) / k^3) \\ Michel Marcus, Nov 11 2021

Formula

Equals (log(2) * zeta(3) + 3 * zeta'(3)) / 4.