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A248589 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. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.1 Geometric probability constants, p. 481.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

Eric Weisstein's MathWorld, Square Point Picking

FORMULA

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 = Pi^(3/2)/(4*A085565), where A085565 is the lemniscate constant A.

I = sqrt(2)*Pi^2/Gamma(1/4)^2.

EXAMPLE

1.061824136490969662805378287398947131005559644732889212...

MATHEMATICA

RealDigits[Sqrt[2]*Pi^2/Gamma[1/4]^2, 10, 100][[1]]

PROG

(PARI) sqrt(2)*Pi^2/gamma(1/4)^2 \\ G. C. Greubel, Jun 02 2017

CROSSREFS

Cf. A053004, A085565, A096428, A096429.

Sequence in context: A349905 A258404 A244692 * A288493 A195293 A230763

Adjacent sequences:  A248586 A248587 A248588 * A248590 A248591 A248592

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Oct 09 2014

STATUS

approved

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Last modified October 3 22:17 EDT 2022. Contains 357237 sequences. (Running on oeis4.)