A249492 Decimal expansion of rho(a,b), the cross-correlation coefficient of two sides of a random Gaussian triangle (in two dimensions).

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

Offset

0,1

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

Eric Weisstein MathWorld, Gaussian Triangle Picking

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

Cf. A102519, A102520, A102556, A102557, A102558, A102559, A249491.

Sequence in context: A318677 A239327 A021047 * A113649 A307864 A066119

Adjacent sequences: A249489 A249490 A249491 * A249493 A249494 A249495

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Oct 30 2014

Status

approved