A244994 - OEIS

%I #21 Jun 17 2015 04:08:21

%S 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,

%T 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,

%U 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

%N Decimal expansion of p_4(2), the maximum radial probability density of a 4-step uniform random walk.

%H Vincenzo Librandi, <a href="/A244994/b244994.txt">Table of n, a(n) for n = 0..10000</a>

%H Jonathan M. Borwein, Armin Straub, James Wan, and Wadim Zudilin, <a href="http://dx.doi.org/10.4153/CJM-2011-079-2">Densities of Short Uniform Random Walks</a> p. 971, Canad. J. Math. 64(2012), 961-990.

%F 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.

%F p_4(2) = (2^(7/3)*Pi)/(3*sqrt(3)*gamma(2/3)^6).

%F p_4(2) = (2*sqrt(3)*gamma(7/6))/(Pi*gamma(2/3)^2*gamma(5/6)).

%e 0.4942337098873326691781895446664234295749970337337829203516164970635637543...

%t RealDigits[2^(7/3)*Pi/(3*Sqrt[3]*Gamma[2/3]^6), 10, 105] // First

%o (PARI) (2^(7/3)*Pi)/(3*sqrt(3)*gamma(2/3)^6) \\ _Michel Marcus_, Jun 17 2015

%Y Cf. A244995 (p_4(1)).

%K nonn,cons,walk

%O 0,1

%A _Jean-François Alcover_, Jul 09 2014