Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Jul 16 2020 02:31:26
%S 9,4,1,1,5,6,3,2,2,1,9,4,8,3,0,0,8,0,0,5,2,8,0,0,4,1,9,4,3,4,1,8,3,7,
%T 9,3,9,2,6,2,3,1,4,4,0,1,5,5,3,5,3,9,8,0,2,7,6,4,6,6,1,5,7,2,8,8,6,0,
%U 5,1,8,9,8,0,5,3,0,1,7,9,0,6,3,6,1,9,9
%N Decimal expansion of the dimensionless coefficient of the Coulomb self-energy of a uniformly charged three-dimensional cube.
%C Coulomb self-energy of a system of electric charges is the total electrostatic potential energy of interaction between charge elements.
%C For a uniformly charged three-dimensional cube with a total charge Q and an edge length L it is equal to c * k*Q^2/L, where k is the Coulomb constant (A182999) and c is this constant.
%H Orion Ciftja, <a href="https://doi.org/10.1016/j.physleta.2010.12.029">Coulomb self-energy of a uniformly charged three-dimensional cube</a>, Physics Letters A, Vol. 375, No. 3 (2011), pp. 766-767, <a href="https://www.researchgate.net/publication/251584942_Coulomb_self-energy_of_a_uniformly_charged_three-dimensional_cube">alternative link</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Electric_potential_energy">Electric potential energy</a>.
%F Equals (1 + sqrt(2) - 2*sqrt(3))/5 - Pi/3 + log((1 + sqrt(2)) * (2 + sqrt(3))).
%e 0.94115632219483008005280041943418379392623144015535...
%t RealDigits[(1 + Sqrt[2] - 2*Sqrt[3])/5 - Pi/3 + Log[(1 + Sqrt[2])*(2 + Sqrt[3])], 10, 100][[1]]
%o (PARI) (1 + sqrt(2) - 2*sqrt(3))/5 - Pi/3 + log((1+sqrt(2))*(2+sqrt(3))) \\ _Michel Marcus_, Jul 15 2020
%Y Cf. A085469, A182999, A336275.
%K nonn,cons
%O 0,1
%A _Amiram Eldar_, Jul 15 2020