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A244999
Decimal expansion of the moment derivative W_5'(0) associated with the radial probability distribution of a 5-step uniform random walk.
1
5, 4, 4, 4, 1, 2, 5, 6, 1, 7, 5, 2, 1, 8, 5, 5, 8, 5, 1, 9, 5, 8, 7, 8, 0, 6, 2, 7, 4, 5, 0, 2, 7, 6, 7, 6, 6, 6, 6, 0, 5, 2, 8, 0, 2, 0, 2, 8, 5, 2, 7, 4, 4, 2, 2, 8, 7, 0, 2, 8, 4, 9, 3, 9, 0, 2, 1, 4, 3, 6, 9, 1, 4, 2, 9, 2, 6, 6, 8, 3, 8, 7, 0, 5, 8, 4, 9, 2, 4, 1, 5, 7
OFFSET
0,1
LINKS
Jonathan M. Borwein, Armin Straub, James Wan, and Wadim Zudilin, Densities of Short Uniform Random Walks p. 978, Canad. J. Math. 64(2012), 961-990.
FORMULA
W_5'(0) = log(2) - gamma - integral_{x=0..1}((J_0(x)^5-1)/x) - integral_{x>1}(J_0(x)^5/x), where J_0 is the Bessel function of the first kind.
EXAMPLE
0.54441256175218558519587806274502767666605280202852744228702849390214369...
MATHEMATICA
digits = 92; Log[2] - EulerGamma - NIntegrate[(BesselJ[0, x]^5 - 1)/x, {x, 0, 1}, WorkingPrecision -> digits + 20] - NIntegrate[BesselJ[0, x]^5/x, {x, 1, Infinity}, WorkingPrecision -> digits + 20] // RealDigits[#, 10, digits] & // First
CROSSREFS
Sequence in context: A241183 A137240 A243380 * A201129 A261509 A226578
KEYWORD
nonn,cons,walk
AUTHOR
STATUS
approved