The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A249491 Decimal expansion of the expected product of two sides of a random Gaussian triangle (in two dimensions). 6
 3, 3, 4, 1, 2, 2, 3, 3, 0, 5, 1, 3, 8, 8, 1, 4, 5, 5, 7, 5, 3, 2, 3, 7, 5, 5, 8, 1, 2, 6, 5, 0, 4, 9, 0, 5, 9, 8, 5, 0, 2, 4, 5, 6, 6, 8, 0, 9, 7, 2, 9, 4, 2, 7, 5, 8, 2, 3, 2, 4, 0, 0, 9, 9, 1, 2, 3, 1, 4, 6, 3, 5, 4, 7, 6, 1, 6, 4, 2, 4, 0, 2, 0, 0, 6, 4, 7, 7, 6, 6, 2, 0, 2, 9, 0, 9, 9, 5, 5, 3, 2, 2, 6, 5 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 = 1..5000 S. R. Finch, Random Triangles, Jan 21 2010. [Cached copy, with permission of the author] Eric Weisstein MathWorld, Gaussian Triangle Picking FORMULA p = 4*E(1/4) - sqrt(3)*K(-1/3), where E is the complete elliptic integral and K the complete elliptic integral of the first kind. Equals A093728/2. - Altug Alkan, Oct 02 2018 EXAMPLE 3.341223305138814557532375581265049059850245668... MAPLE Re(evalf(4*EllipticE(1/2)-sqrt(3)*EllipticK(I/sqrt(3)), 120)); # Vaclav Kotesovec, Apr 22 2015 MATHEMATICA ek[x_] := EllipticK[x^2/(-1 + x^2)]/Sqrt[1 - x^2]; ee[x_] := EllipticE[x^2]; p = 4*ee[1/2] - (3/2)*ek[1/2]; (* or *) p = 4*EllipticE[1/4] - Sqrt[3]*EllipticK[-1/3]; RealDigits[p, 10, 104] // First RealDigits[ N[ EllipticE[-8], 102]][[1]] (* Altug Alkan, Oct 02 2018 *) RealDigits[3 EllipticE[8/9], 10, 102][[1]] (* Jan Mangaldan, Nov 24 2020 *) PROG (PARI) magm(a, b)=my(eps=10^-(default(realprecision)-5), c); while(abs(a-b)>eps, my(z=sqrt((a-c)*(b-c))); [a, b, c] = [(a+b)/2, c+z, c-z]); (a+b)/2 E(x)=Pi/2/agm(1, sqrt(1-x))*magm(1, 1-x) K(x)=Pi/2/agm(1, sqrt(1-x)) 4*E(1/4) - sqrt(3)*K(-1/3) \\ Charles R Greathouse IV, Aug 02 2018 CROSSREFS Cf. A093728, A102519, A102520, A102556, A102557, A102558, A102559. Sequence in context: A078911 A353417 A082899 * A309888 A245250 A179561 Adjacent sequences: A249488 A249489 A249490 * A249492 A249493 A249494 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Oct 30 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 8 11:46 EST 2023. Contains 367678 sequences. (Running on oeis4.)