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Decimal expansion of the moment derivative W_4'(0) associated with the radial probability distribution of a 4-step uniform random walk.
3

%I #10 Jun 13 2021 05:41:40

%S 4,2,6,2,7,8,3,9,8,8,1,7,5,0,5,7,9,0,9,2,3,5,2,1,4,2,6,5,9,6,1,6,6,8,

%T 7,3,0,5,8,0,0,6,7,6,9,6,2,9,6,3,5,1,0,7,5,4,1,6,0,6,4,5,8,0,2,6,5,2,

%U 9,4,5,1,2,2,9,1,1,6,5,8,1,4,8,9,1,2,4,1,8,8,3,3,2,2,4,2,9,4,3,5,8,5,0,4,8

%N Decimal expansion of the moment derivative W_4'(0) associated with the radial probability distribution of a 4-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.

%H Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 142.

%F W_4'(0) = (7/2)*zeta(3)/Pi^2.

%F W_4'(0) = integral over the square [0,Pi]x[0,Pi] of log(3+2*cos(x)+2*cos(y)+2*cos(x-y)) dx dy.

%e 0.42627839881750579092352142659616687305800676962963510754160645802652945...

%t RealDigits[(7/2)*Zeta[3]/Pi^2, 10, 105] // First

%Y Cf. A244996.

%K nonn,cons,walk

%O 0,1

%A _Jean-François Alcover_, Jul 09 2014