A254140 Decimal expansion of the average reciprocal distance between two points chosen at random in a unit square.

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

Offset: 1

Author

Jean-François Alcover, Jan 26 2015

Keywords

• nonn
• cons
• easy

Examples

			2.97320959824737870252818566763957179801974547921061 ...
		

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, Square Line Picking

Crossrefs

Cf. A091505.

Programs

Mathematica

RealDigits[4/3 - 4*Sqrt[2]/3 + 4*Log[1 + Sqrt[2]], 10, 105] // First

Formula

Integral over a unit square of 1/sqrt((r1-q1)^2 + (r2-q2)^2) dr1 dr2 dq1 dq2 = 4/3 - 4*sqrt(2)/3 + 4*log(1 + sqrt(2)).