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A263492 Decimal expansion of the generalized hypergeometric function 3F2(1/2,1/2,3/2 ; 1,2 ; x) at x=1/4. 1

%I

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

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

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

%N Decimal expansion of the generalized hypergeometric function 3F2(1/2,1/2,3/2 ; 1,2 ; x) at x=1/4.

%C Multiplication with Pi^2/16 gives 0.64977.. = integral_{x=0..infinity} I_1(x)*K_0(x)*K_1(x) dx, where I and K are Modified Bessel Functions. [corrected by _Vaclav Kotesovec_, Apr 10 2016]

%e 1.05337959641476007603489294...

%t RealDigits[HypergeometricPFQ[{1/2, 1/2, 3/2}, {1, 2}, 1/4], 10, 120][[1]] (* _Vaclav Kotesovec_, Apr 10 2016 *)

%t RealDigits[Integrate[16*BesselI[1, x]*BesselK[0, x]*BesselK[1, x]/Pi^2 , {x, 0, Infinity}], 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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Last modified October 21 12:47 EDT 2021. Contains 348155 sequences. (Running on oeis4.)