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A244994 Decimal expansion of p_4(2), the maximum radial probability density of a 4-step uniform random walk. 2
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 (list; constant; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jul 09 2014

STATUS

approved

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Last modified October 23 13:25 EDT 2021. Contains 348214 sequences. (Running on oeis4.)