A389669 Decimal expansion of Sum_{k>=2} (-1)^k * zeta(k) / ((k+1) * (k+2)).

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

Offset

0,2

Comments

Note that the sum in Choi et al. (1995) starts at k = 3, and thus equals this constant minus Pi^2/72.

Links

Table of n, a(n) for n=0..104.

Junesang Choi, The Catalan's constant and series involving the zeta function, Communications of the Korean Mathematical Society, Vol. 13, No. 2 (1998), pp. 435-443. See p. 438, eq. (1.14).

Junesang Choi and H. M. Srivastava, Sums associated with the Zeta function, J. Math. Anal. Appl., Vol. 206, No. 1 (1997), pp. 103-120. See p. 116, eq. (2.63).

Junesang Choi, H. M. Srivastava, and J. R. Quine, Some series involving the zeta function, Bulletin of the Australian Mathematical Society, Vol. 51, No. 3 (1995), pp. 383-393. See eq. (2.33), p. 391.

Formula

Equals 1/2 + gamma/6 - 2*log(A), where gamma is Euler's constant (A001620), and A is the Glaisher-Kinkelin constant (A074962).

Example

0.098693656749353618339912694528172452978953795319583...

Mathematica

RealDigits[1/2 + EulerGamma/6 - 2*Log[Glaisher], 10, 120, -1][[1]]

Prog

(PARI) 1/3 + Euler/6 + 2*zeta'(-1)

Crossrefs

Cf. A001620, A074962, A225746.

Related constants: A321943, A379425, A389666, A389667, A389668, A389670.

Sequence in context: A358661 A129269 A094145 * A388630 A002388 A388835

Adjacent sequences: A389666 A389667 A389668 * A389670 A389671 A389672

Keyword

nonn,cons

Author

Amiram Eldar, Oct 10 2025

Status

approved