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A247447
Decimal expansion of r_(5,1), a constant which is the residue at -4 of the distribution function of the distance travelled in a 5-step uniform random walk.
0
0, 0, 6, 6, 1, 6, 7, 3, 0, 2, 5, 9, 4, 3, 0, 0, 8, 1, 7, 1, 4, 0, 5, 7, 7, 3, 8, 0, 0, 0, 7, 4, 9, 6, 5, 6, 2, 4, 9, 5, 5, 1, 0, 3, 2, 7, 5, 2, 4, 8, 3, 3, 0, 3, 9, 9, 7, 1, 5, 8, 3, 6, 3, 0, 8, 3, 2, 7, 5, 3, 4, 7, 2, 7, 1, 4, 0, 9, 2, 1, 2, 8, 0, 8, 2, 8, 0, 7, 7, 9, 0, 7, 6, 6, 9, 2, 9, 0, 4, 9, 1, 6, 4
OFFSET
0,3
LINKS
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.
FORMULA
r_(5,1) = 13/225*r_(5,0) - 2/(5*Pi^4*r_(5,0)), where r_(5,0) is A244995 (residue at -2).
r_(5,1) = 13/(1800*sqrt(5))*Gamma(1/15)*Gamma(2/15)*Gamma(4/15)*Gamma(8/15)/Pi^4 - 1/sqrt(5)*Gamma(7/15)*Gamma(11/15)*Gamma(13/15)*Gamma(14/15)/Pi^4.
EXAMPLE
0.0066167302594300817140577380007496562495510327524833...
MATHEMATICA
r[5, 0] = (2*Sqrt[15]*Re[HypergeometricPFQ[{1/2, 1/2, 1/2}, {5/6, 7/6}, 125/4]])/Pi^2; r[5, 1] = 13/225*r[5, 0] - 2/(5*Pi^4*r[5, 0]); Join[{0, 0}, RealDigits[r[5, 1], 10, 101] // First]
KEYWORD
nonn,cons,walk
AUTHOR
STATUS
approved