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A336275
Decimal expansion of the dimensionless coefficient of the Coulomb self-energy of a uniformly charged two-dimensional square.
1
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, 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, 3, 2, 7, 1, 6, 1, 3, 5, 9, 8, 0, 8, 1, 6, 4, 3, 3, 8, 2
OFFSET
1,2
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 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.
FORMULA
Equals 2*(1 - sqrt(2))/3 + 2 * log(1 + sqrt(2)).
EXAMPLE
1.486604799123689351264092833819785899009872739605305...
MATHEMATICA
RealDigits[2*(1 - Sqrt[2])/3 + 2*Log[1 + Sqrt[2]], 10, 100][[1]]
PROG
(PARI) 2*(1 - sqrt(2))/3 + 2 * log(1 + sqrt(2)) \\ Michel Marcus, Jul 15 2020
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Jul 15 2020
STATUS
approved