A386712 Decimal expansion of Sum_{k>=2} (zeta(k)-1)/(k+2).

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

Offset: 0

Author

Amiram Eldar, Jul 31 2025

Keywords

• nonn
• cons

Examples

			0.22448062442724777958966024641468693092980998704517...
		

References

• Hari M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier, 2012. See eq. (543), p. 320.

Links

• Ovidiu Furdui, The evaluation of a class of fractional part integrals, Integral Transforms and Special Functions, Vol. 26, No. 8 (2015), pp. 635-641.
• Michael I. Shamos, Shamos's catalog of the real numbers, 2011. See p. 290.
• Hari M. Srivastava and Junesang Choi, Series Associated with the Zeta and Related Functions, Springer Science+Business Media Dordrecht, 2001. See eq. (517), p. 219.

Crossrefs

Cf. A001620 (gamma), A061444, A074962 (A), A225746.

Sum_{k>=2} (zeta(k)-1)/(k+m): A153810 (m=0), A386711 (m=1), this constant (m=2).

Programs

Mathematica

RealDigits[11/6 - EulerGamma/3 - 2*Log[Glaisher] - Log[2*Pi]/2, 10, 120][[1]]

PARI

11/6 - Euler/3 - 2*(1/12-zeta'(-1)) - log(2*Pi)/2

Formula

Equals 11/6 - gamma/3 - 2*log(A) - log(2*Pi)/2, where gamma is Euler's constant and A is the Glaisher-Kinkelin constant (Srivastava and Choi, 2001).

Equals -Sum_{k>=2} (k^2*log(1-1/k) + k + 1/(3*k) + 1/2) (Shamos, 2011).