A242588 Decimal expansion of the expected reciprocal Euclidean distance between two random points in the unit cube.

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

Offset: 1

Author

Jean-François Alcover, May 20 2014

Keywords

• nonn
• cons

Examples

			1.88231264438966016010560083886836758785246288...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.1, p. 480.

Links

• D. H. Bailey, J. M. Borwein, R. E. Crandall, Advances in the theory of box integrals Math. Comp. 79 (2010), 1839-1866, p. 24.
• Eric Weisstein's MathWorld, Cube Point Picking

Crossrefs

Cf. A073012, A097047, A135691.

Programs

Mathematica

2*(1/5*(Sqrt[2] + 1 - 2*Sqrt[3]) - Log[(Sqrt[2] - 1)*(2 - Sqrt[3])] - Pi/3) // RealDigits[#, 10, 100]& // First

Formula

Integral over a unit cube of 1/sqrt((r1-q1)^2 + (r2-q2)^2 + (r3-q3)^2) dr1 dr2 dr3 dq1 dq2 dq3 = 2*(1/5*(sqrt(2) + 1 - 2*sqrt(3)) - log((sqrt(2) - 1)*(2 - sqrt(3))) - Pi/3).