A130590 Decimal expansion of the mean Euclidean distance from a point in the unit 3D cube to a given vertex of the cube.

9, 6, 0, 5, 9, 1, 9, 5, 6, 4, 5, 5, 0, 5, 2, 9, 5, 9, 4, 2, 5, 1, 0, 7, 9, 5, 1, 3, 9, 3, 8, 0, 6, 3, 6, 0, 2, 4, 0, 9, 7, 6, 9, 0, 7, 5, 4, 5, 7, 2, 3, 9, 8, 7, 6, 9, 0, 8, 9, 8, 5, 1, 5, 3, 1, 0, 3, 8, 7, 6, 6, 3, 3, 4, 0, 1, 6, 3, 2, 8, 9, 0, 3, 1, 2, 2, 7, 9, 3, 5, 6, 9, 1, 7, 7, 4, 8, 2, 4, 5, 3, 1, 2, 1, 6

Offset

0,1

Links

Table of n, a(n) for n=0..104.

D. H. Bailey, J. M. Borwein and R. E. Crandall, Box Integrals, J. Comp. Appl. Math., Vol. 206, No. 1 (2007), pp. 196-208.

D. H. Bailey, J. M. Borwein, and R. E. Crandall, Advances in the theory of box integrals, Math. Comp. 79 (271) (2010) 1839-1866, Table 2. [From R. J. Mathar, Oct 13 2010]

Eric Weisstein's World of Mathematics, Box Integral.

Formula

Equals sqrt(3)/4 + log(2+sqrt(3))/2 - Pi/24 = A010527/2 + A065914/2 - A019691.

Equals 2 * A135691. - Amiram Eldar, Jun 04 2023

Example

0.960591956455052959425107951...

Maple

evalf( sqrt(3)/4+log(2+sqrt(3))/2-Pi/24);

Mathematica

RealDigits[Sqrt[3]/4 + Log[2+Sqrt[3]]/2 - Pi/24, 10, 120][[1]] (* Amiram Eldar, Jun 04 2023 *)

Crossrefs

Cf. A010527, A019691, A065914, A135691.

Analogous constants: A244921 (square), A254979 (4-cube).

Sequence in context: A154161 A336001 A361601 * A197413 A021055 A199067

Adjacent sequences: A130587 A130588 A130589 * A130591 A130592 A130593

Keyword

cons,easy,nonn

Author

R. J. Mathar, Aug 10 2007

Extensions

Name corrected by Amiram Eldar, Jun 04 2023

Status

approved