A390067 Decimal expansion of Sum_{k>=2} (-1)^k * zeta(k) / (4^k * (k+1)).

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

Offset

0,2

References

H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights, 2011. See p. 339, eq. (666).

Links

Table of n, a(n) for n=0..105.

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. 441, eq. (3.6).

Formula

Equals 1 + gamma/8 - G/Pi - log(2 * Pi * A^9 / Gamma(1/4)^2)/2, where gamma is Euler's constant (A001620), G is Catalan's constant (A006752), and A is the Glaisher-Kinkelin constant (A074962).

Example

0.03027989892324836156507178751349214864202014297332...

Mathematica

RealDigits[1 + EulerGamma/8 - Catalan/Pi - Log[2*Pi]/2 - 9*Log[Glaisher]/2 + Log[Gamma[1/4]], 10, 120, -1][[1]]

Prog

(PARI) 5/8 + Euler/8 - Catalan/Pi - log(2*Pi)/2 + 9*zeta'(-1)/2 + log(gamma(1/4))

Crossrefs

Cf. A001620, A006752, A061444, A068466, A074962, A143233, A225746, A378910, A390068, A390069.

Sequence in context: A248820 A085550 A223139 * A302278 A302728 A302528

Adjacent sequences: A390064 A390065 A390066 * A390068 A390069 A390070

Keyword

nonn,cons

Author

Amiram Eldar, Oct 23 2025

Status

approved