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A242588
Decimal expansion of the expected reciprocal Euclidean distance between two random points in the unit cube.
1
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
1,2
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
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).
EXAMPLE
1.88231264438966016010560083886836758785246288...
MATHEMATICA
2*(1/5*(Sqrt[2] + 1 - 2*Sqrt[3]) - Log[(Sqrt[2] - 1)*(2 - Sqrt[3])] - Pi/3) // RealDigits[#, 10, 100]& // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved