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A091506
Decimal expansion of (2 + sqrt(2) + 5*arcsinh(1))/9.
2
8, 6, 9, 0, 0, 9, 0, 5, 5, 2, 7, 4, 5, 3, 4, 4, 6, 3, 8, 8, 4, 9, 7, 0, 5, 9, 4, 3, 4, 5, 4, 0, 6, 6, 2, 4, 8, 5, 6, 7, 1, 9, 2, 7, 9, 6, 3, 1, 6, 8, 0, 5, 6, 9, 6, 6, 0, 3, 5, 0, 8, 6, 4, 5, 8, 4, 1, 7, 9, 8, 2, 2, 1, 7, 4, 6, 9, 3, 0, 5, 3, 1, 1, 3, 2, 1, 3, 5, 5, 4, 8, 7, 5, 4, 3, 5, 7, 5, 4, 1, 1, 3
OFFSET
0,1
COMMENTS
Average distance between two points chosen at random on two different edges of a unit square.
REFERENCES
Jonathan Borwein, David Bailey, and Roland Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery. Natick: A K Peters (2004): p. 66, Example 57(a).
LINKS
D. H. Bailey, J. M. Borwein, V. Kapoor and E. Weisstein, Ten Problems in Experimental Mathematics
Eric Weisstein's World of Mathematics, Square Line Picking
FORMULA
Also equals (2 + sqrt(2) + 5*log(1 + sqrt(2)))/9. - Jean-François Alcover, Feb 14 2014
James D. Klein proved that this constant is equal to 2/3*int(int(sqrt(x^2 + y^2), x = 0..1), y = 0..1) + 1/3*int(int(sqrt(1 + (y - u)^2), u = 0..1), y = 0..1). - John M. Campbell, Apr 02 2016
EXAMPLE
0.86900905527453446388497059434540662485671927963168056966035...
MATHEMATICA
RealDigits[(2 + Sqrt[2] + 5ArcSinh[1])/9, 10, 120][[1]] (* Harvey P. Dale, May 22 2013 *)
PROG
(PARI) (2 + sqrt(2) + 5*asinh(1))/9 \\ G. C. Greubel, Aug 17 2018
(Magma) SetDefaultRealField(RealField(100)); (2 + Sqrt(2) + 5*Argsinh(1))/9; // G. C. Greubel, Aug 17 2018
CROSSREFS
Cf. A091505.
Sequence in context: A110214 A305709 A093721 * A021539 A084893 A019939
KEYWORD
nonn,easy,cons
AUTHOR
Eric W. Weisstein, Jan 16 2004
EXTENSIONS
Broken link fixed by John M. Campbell, Apr 02 2016
STATUS
approved