

A249492


Decimal expansion of rho(a,b), the crosscorrelation coefficient of two sides of a random Gaussian triangle (in two dimensions).


3



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

0,1


COMMENTS

Coordinates are independent normally distributed random variables with mean 0 and variance 1.


LINKS

Steven R. Finch, Random Triangles, January 21, 2010. [Cached copy, with permission of the author]


FORMULA

rho = (p  Pi)/(4  Pi), where p is A249491, the expected value of the product of two sides.


EXAMPLE

0.23255934654317823447309035975033389931043501543502...


MAPLE

Re(evalf((4*EllipticE(1/2)  sqrt(3)*EllipticK(I/sqrt(3))  Pi)/(4  Pi), 120)); # Vaclav Kotesovec, Apr 22 2015


MATHEMATICA

p = 4*EllipticE[1/4]  Sqrt[3]*EllipticK[1/3]; rho = (p  Pi)/(4  Pi); RealDigits[rho, 10, 103] // First
RealDigits[(3 EllipticE[8/9]  Pi)/(4  Pi), 10, 103][[1]] (* Jan Mangaldan, Nov 26 2020 *)


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



