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%I #8 Aug 27 2014 14:31:47
%S 2,1,4,2,2,0,4,4,9,8,5,2,5,6,6,3,4,6,8,0,1,3,9,1,9,7,8,4,7,0,1,9,6,5,
%T 0,2,0,1,2,0,6,4,5,8,0,1,7,9,1,8,0,0,0,6,9,1,9,3,5,5,6,3,8,0,6,4,6,4,
%U 9,9,8,8,3,2,1,7,9,0,4,8,3,3,9,9,0,7,9,2,7,8,4,0,3,3,3,5,7,8,4,2,4,0,8,9,1
%N Decimal expansion of the moment derivative W_3'(2) associated with the radial probability distribution of a 3-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 Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/ClausensIntegral.html">Clausen's Integral</a>
%F W_3'(2) = 2 + (3/Pi)*Cl2(Pi/3) - 3*sqrt(3)/(2*Pi), where Cl2 is the Clausen function.
%F W_3'(2) = 2 + 3*W_3'(0) - 3*sqrt(3)/(2*Pi).
%e 2.1422044985256634680139197847019650201206458017918000691935563806464998832...
%t Clausen2[x_] := Im[PolyLog[2, Exp[x*I]]]; RealDigits[2 + (3/Pi)*Clausen2[Pi/3] - 3*Sqrt[3]/(2*Pi), 10, 105] // First
%o (PARI) 2 + 3*imag(polylog(2, exp(Pi*I/3)))/Pi - 3*sqrt(3)/2/Pi \\ _Charles R Greathouse IV_, Aug 27 2014
%Y Cf. A244996.
%K nonn,cons,walk
%O 1,1
%A _Jean-François Alcover_, Jul 10 2014
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