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A244995 Decimal expansion of p_4(1), a particular radial probability density of a 4-step uniform random walk. 2
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 (list; constant; graph; refs; listen; history; text; internal format)
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 A099887

Adjacent sequences:  A244992 A244993 A244994 * A244996 A244997 A244998

KEYWORD

nonn,cons,walk

AUTHOR

Jean-Fran├žois Alcover, Jul 09 2014

STATUS

approved

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Last modified January 23 16:17 EST 2021. Contains 340385 sequences. (Running on oeis4.)