OFFSET
0,1
REFERENCES
L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (312).
LINKS
Michael I. Shamos, Shamos's catalog of the real numbers (2011).
FORMULA
Equals 2 * Pi^2 / 3^3.
Equals 1 + Sum_{k>=1} ( (-1)^k/(3*k-1)^2 + (-1)^k/(3*k+1)^2 ).
Equals Integral_{0..infinity} x * log(x) / (x^3+1) dx.
Equals Integral_{0..1} (1+x) * log(x) / (1-x^3) dx.
Equals Integral_{0..infinity} x * (1-exp(-x)) / (exp(x) * (1+exp(-3*x))) dx.
EXAMPLE
0.73108180748810063843218451850...
MATHEMATICA
RealDigits[(2 Pi^2)/27, 10, 120][[1]] (* Harvey P. Dale, Dec 04 2022 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Sean A. Irvine, Aug 07 2021
STATUS
approved