OFFSET
0,1
COMMENTS
The complement (A239097) is gamma(0,2) = lim_{x -> oo} (Sum_{0<n<=x, n even} (1/n - log(x)/2) = (A001620 - A002162)/2 = -0.05796575... - R. J. Mathar, Sep 06 2013
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
M. L. Glasser, A note on Beukers's and related integrals, Amer. Math. Monthly 126(4) (2019), 361-363.
J. C. Lagarias, Euler's constant: Euler's work and modern developments, arXiv:1303.1856 [math.NT], 2013. See Section 3.8.
D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975), 125-142.
FORMULA
Equals lim_{x -> oo} (Sum_{0<n<=x, n odd} 1/n - log(x)/2).
From Amiram Eldar, Jun 30 2020: (Start)
Equals -Integral_{x=0..1} log(log(1/x))*x dx.
Equals -Integral_{x=0..oo} exp(-2*x)*log(x) dx. (End)
Equals Integral_{x=0..1, y=0..1} log(-log(x*y))*x*y/log(x*y) dx dy. (Apply Theorem 1 or Theorem 2 of Glasser (2019) to one of Amiram Eldar's integrals.) - Petros Hadjicostas, Jun 30 2020
EXAMPLE
0.63518142273073908501187210577028949955882973515008942646322...
MAPLE
(gamma+log(2))/2 ; evalf(%) ;
MATHEMATICA
RealDigits[(EulerGamma+Log[2])/2, 10, 120][[1]] (* Harvey P. Dale, Dec 26 2013 *)
PROG
(PARI) (Euler+log(2))/2 \\ Charles R Greathouse IV, Jul 21 2015
(Magma) SetDefaultRealField(RealField(100)); R:= RealField();
(EulerGamma + Log(2))/2; // G. C. Greubel, Aug 27 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
R. J. Mathar, Aug 31 2013
STATUS
editing