A346933 - OEIS

%I #12 Aug 05 2024 13:50:52

%S 7,3,1,0,8,1,8,0,7,4,8,8,1,0,0,6,3,8,4,3,2,1,8,4,5,1,8,5,0,9,3,4,4,5,

%T 2,8,5,4,1,7,5,5,5,1,1,6,4,7,4,6,5,9,7,2,3,2,6,9,1,4,7,6,8,6,0,8,8,9,

%U 2,2,0,9,0,6,8,0,8,9,2,7,7,2,5,9,3,9,0

%N Decimal expansion of 2 * Pi^2 / 27.

%D L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (312).

%H Michael I. Shamos, <a href="https://citeseerx.ist.psu.edu/pdf/ae33a269baba5e8b1038e719fb3209e8a00abec5">Shamos's catalog of the real numbers</a> (2011).

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals 2 * Pi^2 / 3^3.

%F Equals 1 + Sum_{k>=1} ( (-1)^k/(3*k-1)^2 + (-1)^k/(3*k+1)^2 ).

%F Equals Integral_{0..infinity} x * log(x) / (x^3+1) dx.

%F Equals Integral_{0..1} (1+x) * log(x) / (1-x^3) dx.

%F Equals Integral_{0..infinity} x * (1-exp(-x)) / (exp(x) * (1+exp(-3*x))) dx.

%e 0.73108180748810063843218451850...

%t RealDigits[(2 Pi^2)/27,10,120][[1]] (* _Harvey P. Dale_, Dec 04 2022 *)

%Y Cf. A346932, A346931, A346930, A346929.

%K nonn,cons

%O 0,1

%A _Sean A. Irvine_, Aug 07 2021