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%I #7 Jul 16 2020 02:31:39
%S 1,4,8,6,6,0,4,7,9,9,1,2,3,6,8,9,3,5,1,2,6,4,0,9,2,8,3,3,8,1,9,7,8,5,
%T 8,9,9,0,0,9,8,7,2,7,3,9,6,0,5,3,0,5,4,3,9,3,8,8,8,0,4,7,2,5,3,1,2,9,
%U 3,2,7,1,6,1,3,5,9,8,0,8,1,6,4,3,3,8,2
%N Decimal expansion of the dimensionless coefficient of the Coulomb self-energy of a uniformly charged two-dimensional square.
%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 two-dimensional square with a total charge Q and a side 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.2009.12.017">Coulomb self-energy and electrostatic potential of a uniformly charged square in two dimensions</a>, Physics Letters A, Vol. 374, No. 7 (2010), pp. 981-983, <a href="https://www.researchgate.net/publication/238921287_Coulomb_self-energy_and_electrostatic_potential_of_a_uniformly_charged_square_in_two_dimensions">alternative link</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Electric_potential_energy">Electric potential energy</a>.
%F Equals 2*(1 - sqrt(2))/3 + 2 * log(1 + sqrt(2)).
%e 1.486604799123689351264092833819785899009872739605305...
%t RealDigits[2*(1 - Sqrt[2])/3 + 2*Log[1 + Sqrt[2]], 10, 100][[1]]
%o (PARI) 2*(1 - sqrt(2))/3 + 2 * log(1 + sqrt(2)) \\ _Michel Marcus_, Jul 15 2020
%Y Cf. A085469, A182999, A336274.
%K nonn,cons
%O 1,2
%A _Amiram Eldar_, Jul 15 2020