A346933 Decimal expansion of 2 * Pi^2 / 27.

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

Offset: 0

Author

Sean A. Irvine, Aug 07 2021

Keywords

• nonn
• cons

Examples

			0.73108180748810063843218451850...
		

References

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

Links

• Michael I. Shamos, Shamos's catalog of the real numbers (2011).
• Index entries for transcendental numbers

Crossrefs

Cf. A346932, A346931, A346930, A346929.

Programs

Mathematica

RealDigits[(2 Pi^2)/27,10,120][[1]] (* Harvey P. Dale, Dec 04 2022 *)

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.