login
A336274
Decimal expansion of the dimensionless coefficient of the Coulomb self-energy of a uniformly charged three-dimensional cube.
4
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, 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, 5, 1, 8, 9, 8, 0, 5, 3, 0, 1, 7, 9, 0, 6, 3, 6, 1, 9, 9
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
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