OFFSET
0,1
LINKS
David H. Bailey, Jonathan M. Borwein and Richard E. Crandall, On the Khintchine Constant, Mathematics of Computation, Vol. 66, No. 217 (1997), pp. 417-431, see p. 419; alternative link, p. 4.
FORMULA
Integral_{0..1} log(1-x^2)/(x*(1+x)) dx = -log(2)^2.
Integral_{0..1} log(log(1/x))/(x+sqrt(x)) dx = log(2)^2.
Equals Sum_{k>=1} H(k)/(2^k * (k+1)) = 2 * Sum_{k>=1} (-1)^(k+1) * H(k)/(k+1), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number. - Amiram Eldar, Aug 05 2020
Equals Sum_{n >= 0} (-1)^n/(2^(n+1)*(n+1)^2*binomial(2*n+1,n)). See my entry in A002544 dated Apr 18 2017. Cf. A091476. - Peter Bala, Jan 30 2023
EXAMPLE
0.480453013918201424667102526326664971730552951594545586866864...
MATHEMATICA
RealDigits[Log[2]^2, 10, 103] // First
PROG
(PARI) log(2)^2 \\ Charles R Greathouse IV, Apr 20 2016
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Mar 24 2015
STATUS
approved