OFFSET
0,1
REFERENCES
H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights (2011) p. 272.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
Eric Weisstein's MathWorld, Riemann Zeta Function
Wikipedia, Riemann Zeta Function
FORMULA
Equals (1/2)*log(Pi) - EulerGamma/2.
Equals Sum_{k>0} (-1)^(k+1)*(H(k)-log(k)-EulerGamma), where H(k) is the k-th harmonic number.
Equals -Sum_{k>=1} (1/(2*k) + log(1 - 1/(2*k))). - Amiram Eldar, Jul 22 2020
EXAMPLE
0.2837571104739336567684576306353281403025677384876939863539279...
MATHEMATICA
RealDigits[(1/2)*Log[Pi] - EulerGamma/2, 10, 105] // First
PROG
(PARI) log(Pi)/2 - Euler/2 \\ Michel Marcus, Apr 13 2015
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (Log(Pi(R)) - EulerGamma(R))/2; // G. C. Greubel, Sep 04 2018
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Apr 13 2015
STATUS
approved