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A248589
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Decimal expansion of I, a constant appearing (as I^2) in the asymptotic variance of the area of the convex hull of random points in the unit square.
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1
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1, 0, 6, 1, 8, 2, 4, 1, 3, 6, 4, 9, 0, 9, 6, 9, 6, 6, 2, 8, 0, 5, 3, 7, 8, 2, 8, 7, 3, 9, 8, 9, 4, 7, 1, 3, 1, 0, 0, 5, 5, 5, 9, 6, 4, 4, 7, 3, 2, 8, 8, 9, 2, 1, 2, 0, 4, 0, 5, 0, 1, 5, 1, 8, 3, 3, 8, 9, 8, 3, 3, 4, 5, 5, 6, 1, 2, 1, 1, 6, 1, 2, 4, 1, 3, 6, 9, 0, 0, 1, 0, 4, 2, 5, 9, 4, 5, 9, 0, 2
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OFFSET
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1,3
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.1 Geometric probability constants, p. 481.
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LINKS
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FORMULA
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I = sqrt(Pi/8)*(2-integral_{1..infinity} (sqrt(1+s^2)-s)*s^(-3/2) ds).
I = sqrt(Pi/2)*A053004, where A053004 is the arithmetic-geometric mean of 1 and sqrt(2).
I = sqrt(2)*Pi^2/Gamma(1/4)^2.
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EXAMPLE
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1.061824136490969662805378287398947131005559644732889212...
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MATHEMATICA
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RealDigits[Sqrt[2]*Pi^2/Gamma[1/4]^2, 10, 100][[1]]
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PROG
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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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