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%I #19 Oct 01 2022 01:03:33
%S 0,1,4,6,2,4,4,5,3,1,6,2,6,2,8,8,0,4,7,6,0,2,8,3,6,2,1,5,5,8,5,8,1,5,
%T 0,9,5,7,4,0,2,5,5,6,0,1,8,0,2,1,4,0,7,0,7,1,9,9,8,1,0,9,7,7,5,2,6,8,
%U 9,3,0,0,9,8,2,3,4,2,2,6,0,1,4,2,4,1,5,7,1,5,5,6,0,2,0,7,2,1,9,0,8,2,6,5,7
%N Decimal expansion of phi_3(3) = sqrt(3)/(12*Pi^2), an auxiliary constant in the computation of the radial density of a 4-step uniform random walk.
%H Vincenzo Librandi, <a href="/A244993/b244993.txt">Table of n, a(n) for n = 0..10001</a>
%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. 969, Canad. J. Math. 64(2012), 961-990.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F phi_3(x) = (sqrt(3) * 2F1(1/3, 2/3; 1; (x^2*(9-x^2)^2)/(3+x^2)^3))/(Pi^2*(3+x^2)), where 2F1 is the hypergeometric function.
%e 0.0146244531626288047602836215585815095740255601802140707199810977526893...
%p Digits:=100: evalf(sqrt(3)/(12*Pi^2)); # _Wesley Ivan Hurt_, Jul 10 2014
%t Join[{0}, RealDigits[Sqrt[3]/(12*Pi^2), 10, 104] // First]
%K nonn,cons,walk
%O 0,3
%A _Jean-François Alcover_, Jul 09 2014
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