A386711 Decimal expansion of Sum_{k>=2} (zeta(k)-1)/(k+1).
2, 9, 2, 4, 5, 3, 6, 3, 4, 3, 4, 4, 5, 6, 0, 8, 2, 7, 9, 1, 6, 4, 1, 4, 2, 1, 8, 5, 5, 3, 1, 8, 1, 1, 4, 4, 6, 1, 7, 5, 2, 2, 8, 5, 8, 3, 9, 2, 2, 5, 4, 7, 8, 7, 7, 7, 9, 9, 6, 4, 8, 4, 2, 0, 7, 4, 8, 0, 0, 4, 4, 0, 6, 8, 3, 9, 0, 7, 2, 6, 6, 8, 3, 6, 7, 8, 3, 1, 6, 9, 7, 1, 8, 1, 7, 2, 4, 2, 7, 6, 2, 0, 6, 7, 8, 6, 2, 9, 7, 5, 0, 4, 6, 2, 1, 2, 1, 3, 1, 3
Offset: 0
Examples
0.29245363434456082791641421855318114461752285839225...
References
- Hari M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier, 2012. See eq. (500), p. 314.
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. 348.
- Hari M. Srivastava and Junesang Choi, Series Associated with the Zeta and Related Functions, Springer Science+Business Media Dordrecht, 2001. See eq. (474), p. 213.
Crossrefs
Programs
-
Mathematica
RealDigits[3/2 - EulerGamma/2 - Log[2*Pi]/2, 10, 120][[1]]
-
PARI
3/2 - Euler/2 - log(2*Pi)/2
Formula
Equals 3/2 - gamma/2 - log(2*Pi)/2 (Srivastava and Choi, 2001).
Equals -Sum_{k>=2} (k*log(1-1/k) + 1 + 1/(2*k)) (Shamos, 2011).