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

0,1

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.

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)).

Example

0.4942337098873326691781895446664234295749970337337829203516164970635637543...

Mathematica

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

Prog

(PARI) (2^(7/3)*Pi)/(3*sqrt(3)*gamma(2/3)^6) \\ Michel Marcus, Jun 17 2015

Crossrefs

Cf. A244995 (p_4(1)).

Sequence in context: A013669 A085365 A019767 * A021091 A096415 A189510

Adjacent sequences: A244991 A244992 A244993 * A244995 A244996 A244997

Keyword

nonn,cons,walk

Author

Jean-François Alcover, Jul 09 2014

Status

approved