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

1,2

Links

Table of n, a(n) for n=1..57.

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.

Example

1.435062...

Prog

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

Crossrefs

Cf. A073002 (eps=0).

Sequence in context: A175325 A223525 A205446 * A152191 A292612 A316254

Adjacent sequences: A343916 A343917 A343918 * A343920 A343921 A343922

Keyword

nonn,cons

Author

R. J. Mathar, May 04 2021

Status

approved