A343919 Decimal expansion of Sum_{k>=1} log(k+1/2)/k^2 .

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

Offset: 1

Author

R. J. Mathar, May 04 2021

Keywords

• nonn
• cons

Examples

			1.435062...
		

Crossrefs

Cf. A073002 (eps=0).

Programs

PARI

sumpos(k=1, log(k+1/2)/k^2) \\ Michel Marcus, May 04 2021

Formula

Sum_{k >=1 } log(k+eps)/k^2 = -Zeta'(2) - Sum_{i=1} (-eps)^i *Zeta(i+2)/i at eps=1/2, weighted sum over Riemann-Zeta.