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A091505
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Decimal expansion of (2 + sqrt(2) + 5*arcsinh(1))/15.
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9
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5, 2, 1, 4, 0, 5, 4, 3, 3, 1, 6, 4, 7, 2, 0, 6, 7, 8, 3, 3, 0, 9, 8, 2, 3, 5, 6, 6, 0, 7, 2, 4, 3, 9, 7, 4, 9, 1, 4, 0, 3, 1, 5, 6, 7, 7, 7, 9, 0, 0, 8, 3, 4, 1, 7, 9, 6, 2, 1, 0, 5, 1, 8, 7, 5, 0, 5, 0, 7, 8, 9, 3, 3, 0, 4, 8, 1, 5, 8, 3, 1, 8, 6, 7, 9, 2, 8, 1, 3, 2, 9, 2, 5, 2, 6, 1, 4, 5, 2, 4, 6, 7
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OFFSET
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0,1
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COMMENTS
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Or equally, decimal expansion of (2 + sqrt(2) + 5*log(1+sqrt(2)))/15.
Average distance between two points chosen at random in a unit square.
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, Sections 8.1 p. 479 and 8.5 p.498.
L. A. Santalo, Integral Geometry and Geometric Probability, Addison-Wesley, 1976, see p. 49.
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LINKS
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EXAMPLE
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0.5214054331647206783309823566...
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MATHEMATICA
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RealDigits[(2+Sqrt[2]+5ArcSinh[1])/15, 10, 120][[1]] (* Harvey P. Dale, Jul 18 2011 *)
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PROG
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(PARI) (2 + sqrt(2) + 5*asinh(1))/15 \\ G. C. Greubel, Jan 11 2017
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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