A263490 - OEIS

%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