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

Author

Jean-François Alcover, Jul 09 2014

Keywords

• nonn
• cons
• walk

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)).