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%I #11 Apr 10 2016 05:44:50
%S 1,0,3,5,1,2,0,6,6,1,4,2,5,6,4,8,9,8,1,0,4,5,9,5,7,5,5,1,4,5,0,8,6,2,
%T 8,4,9,9,7,4,9,4,8,7,3,2,4,4,9,8,5,9,5,7,0,6,9,1,6,1,7,7,5,7,7,1,3,6,
%U 2,0,0,0,7,7,7,0,2,3,5,5,4,2,9,4,7,5,0,2,0,5,4,0,1,3,0,3,7,6,8,9,9
%N Decimal expansion of the generalized hypergeometric function 3F2(1/2,1/2,1/2 ; 1,1; x) at x=1/4.
%C Multiplication with Pi^2/4 gives 2.554057.. = integral_{x=0..infinity} I_0(x) *K_0(x)^2 dx, where I and K are Modified Bessel Functions.
%F Square of A243308.
%F From _Vaclav Kotesovec_, Apr 10 2016: (Start)
%F Equals 3^(1/2) * Gamma(1/3)^6 / (2^(8/3) * Pi^4).
%F Equals Gamma(1/6)^3 / (3 * 2^(5/3) * Pi^(5/2)).
%F (End)
%e 1.0351206614256489810459575514...
%p evalf(4*EllipticK(sqrt(2-sqrt(3))/2)^2 / Pi^2, 120); # _Vaclav Kotesovec_, Apr 10 2016
%t RealDigits[HypergeometricPFQ[{1/2, 1/2, 1/2}, {1, 1}, 1/4], 10, 120][[1]] (* _Vaclav Kotesovec_, Apr 10 2016 *)
%t RealDigits[4*EllipticK[(2 - Sqrt[3])/4]^2 / Pi^2, 10, 120][[1]] (* _Vaclav Kotesovec_, Apr 10 2016 *)
%K cons,nonn
%O 1,3
%A _R. J. Mathar_, Oct 19 2015
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