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%I #8 Jul 10 2014 02:34:07
%S 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,
%T 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,
%U 3,6,9,1,4,2,9,2,6,6,8,3,8,7,0,5,8,4,9,2,4,1,5,7
%N Decimal expansion of the moment derivative W_5'(0) associated with the radial probability distribution of a 5-step uniform random walk.
%H Jonathan M. Borwein, Armin Straub, James Wan, and Wadim Zudilin, <a href="http://dx.doi.org/10.4153/CJM-2011-079-2">Densities of Short Uniform Random Walks</a> p. 978, Canad. J. Math. 64(2012), 961-990.
%F 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.
%e 0.54441256175218558519587806274502767666605280202852744228702849390214369...
%t 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
%Y Cf. A244996, A244997.
%K nonn,cons,walk
%O 0,1
%A _Jean-François Alcover_, Jul 09 2014
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