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Decimal expansion of the dimensionless coefficient of the Coulomb self-energy of a uniformly charged three-dimensional cube.
4

%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