A336274 Decimal expansion of the dimensionless coefficient of the Coulomb self-energy of a uniformly charged three-dimensional cube.

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

Table of n, a(n) for n=0..86.

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

Cf. A085469, A182999, A336275.

Sequence in context: A355282 A270309 A010158 * A286229 A242611 A098454

Adjacent sequences: A336271 A336272 A336273 * A336275 A336276 A336277

Keyword

nonn,cons

Author

Amiram Eldar, Jul 15 2020

Status

approved