OFFSET
0,1
COMMENTS
Coulomb self-energy of a system of electric charges is the total electrostatic potential energy of interaction between charge elements.
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.
LINKS
Orion Ciftja, Coulomb self-energy of a uniformly charged three-dimensional cube, Physics Letters A, Vol. 375, No. 3 (2011), pp. 766-767, alternative link.
Wikipedia, Electric potential energy.
FORMULA
Equals (1 + sqrt(2) - 2*sqrt(3))/5 - Pi/3 + log((1 + sqrt(2)) * (2 + sqrt(3))).
EXAMPLE
0.94115632219483008005280041943418379392623144015535...
MATHEMATICA
RealDigits[(1 + Sqrt[2] - 2*Sqrt[3])/5 - Pi/3 + Log[(1 + Sqrt[2])*(2 + Sqrt[3])], 10, 100][[1]]
PROG
(PARI) (1 + sqrt(2) - 2*sqrt(3))/5 - Pi/3 + log((1+sqrt(2))*(2+sqrt(3))) \\ Michel Marcus, Jul 15 2020
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Jul 15 2020
STATUS
approved