A244994 Decimal expansion of p_4(2), the maximum radial probability density of a 4-step uniform random walk.
4, 9, 4, 2, 3, 3, 7, 0, 9, 8, 8, 7, 3, 3, 2, 6, 6, 9, 1, 7, 8, 1, 8, 9, 5, 4, 4, 6, 6, 6, 4, 2, 3, 4, 2, 9, 5, 7, 4, 9, 9, 7, 0, 3, 3, 7, 3, 3, 7, 8, 2, 9, 2, 0, 3, 5, 1, 6, 1, 6, 4, 9, 7, 0, 6, 3, 5, 6, 3, 7, 5, 4, 3, 0, 4, 2, 4, 7, 3, 6, 0, 6, 4, 7, 5, 6, 2, 3, 3, 8, 4, 3, 7, 7, 0, 7, 1, 7, 8, 2, 9, 4, 4, 2, 7
Offset: 0
Examples
0.4942337098873326691781895446664234295749970337337829203516164970635637543...
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Jonathan M. Borwein, Armin Straub, James Wan, and Wadim Zudilin, Densities of Short Uniform Random Walks p. 971, Canad. J. Math. 64(2012), 961-990.
Crossrefs
Cf. A244995 (p_4(1)).
Programs
-
Mathematica
RealDigits[2^(7/3)*Pi/(3*Sqrt[3]*Gamma[2/3]^6), 10, 105] // First
-
PARI
(2^(7/3)*Pi)/(3*sqrt(3)*gamma(2/3)^6) \\ Michel Marcus, Jun 17 2015
Formula
p_4(x) = (2*sqrt(16-x^2)*Re(3F2(1/2, 1/2, 1/2; 5/6, 7/6; (16-x^2)^3/(108*x^4))))/(Pi^2*x) where 3F2 is the hypergeometric function.
p_4(2) = (2^(7/3)*Pi)/(3*sqrt(3)*gamma(2/3)^6).
p_4(2) = (2*sqrt(3)*gamma(7/6))/(Pi*gamma(2/3)^2*gamma(5/6)).