A244995 Decimal expansion of p_4(1), a particular radial probability density of a 4-step uniform random walk.

3, 2, 9, 9, 3, 3, 8, 0, 1, 0, 6, 0, 0, 6, 4, 0, 5, 9, 0, 3, 9, 7, 9, 0, 6, 5, 2, 2, 8, 6, 9, 5, 2, 9, 6, 4, 6, 9, 3, 6, 8, 3, 0, 4, 8, 0, 7, 5, 8, 3, 4, 2, 7, 7, 3, 6, 0, 2, 6, 0, 3, 9, 3, 6, 2, 6, 0, 2, 7, 5, 7, 4, 2, 5, 7, 2, 6, 4, 4, 0, 5, 8, 4, 2, 3, 3, 4, 1, 5, 5, 1, 7, 2, 2, 6, 7, 4, 9, 4, 8, 8, 9, 4, 3

Offset

0,1

Links

Table of n, a(n) for n=0..103.

Jonathan M. Borwein, Armin Straub, James Wan, and Wadim Zudilin, Densities of Short Uniform Random Walks p. 974, Canad. J. Math. 64(2012), 961-990.

MathOverflow, Integral_{0..infinity} x*[J_0(x)]^5 dx: source and context, if any?

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(1) = (2*sqrt(15)*Re(3F2(1/2, 1/2, 1/2; 5/6, 7/6; 125/4)))/Pi^2.

p_4(1) = (1/(2*Pi^2))*sqrt((gamma(1/15)*gamma(2/15)*gamma(4/15)*gamma(8/15))/(5*gamma(7/15)*gamma(11/15)*gamma(13/15)*gamma(14/15))).

Equals Gamma(1/15) * Gamma(2/15) * Gamma(4/15) * Gamma(8/15) / (8*sqrt(5)*Pi^4). - Vaclav Kotesovec, Jun 10 2019

Example

0.329933801060064059039790652286952964693683048075834277360260393626...

Maple

evalf(GAMMA(1/15)*GAMMA(2/15)*GAMMA(4/15)*GAMMA(8/15) / (8*sqrt(5)*Pi^4), 120); # Vaclav Kotesovec, Jun 10 2019

Mathematica

RealDigits[(2*Sqrt[15]*Re[HypergeometricPFQ[{1/2, 1/2, 1/2}, {5/6, 7/6}, 125/4]])/Pi^2, 10, 104] // First

Crossrefs

Sequence in context: A199455 A287768 A197831 * A152049 A246788 A365278

Adjacent sequences: A244992 A244993 A244994 * A244996 A244997 A244998

Keyword

nonn,cons,walk

Author

Jean-François Alcover, Jul 09 2014

Status

approved