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%I #7 Oct 09 2017 12:21:10
%S 2,6,5,8,1,3,4,9,1,6,5,0,8,6,4,0,8,7,1,7,7,5,0,5,2,0,4,9,1,9,4,6,0,3,
%T 9,8,6,3,2,8,2,6,1,6,6,4,0,3,6,9,4,0,8,5,0,5,0,4,6,2,5,5,4,4,2,4,5,0,
%U 1,3,2,4,0,9,2,4,0,3,9,8,3,2,6,6,1,6,2,6,5,1,9,1,1,8,4,5,2,8,2,1,7,4,3,1,1
%N Decimal expansion of Pi * 2F3(1/2,1/2; 3/2,3/2,3/2; -Pi^2/4).
%C The absolute value of the integral of sin(Pi*x)*log(x)/x from x=0 to 1.
%H R. J. Mathar, <a href="http://arxiv.org/abs/0912.3844">Numerical evaluation of the oscillatory integral...</a>, arXiv:0912.3844 [math.CA], App. B.
%e 2.6581349...
%p evalf(Pi*hypergeom([1/2,1/2],[3/2,3/2,3/2],-Pi^2/4)) ;
%t Pi*HypergeometricPFQ[{1/2, 1/2}, {3/2, 3/2, 3/2}, -Pi^2/4] // RealDigits[#, 10, 105]& // First (* _Jean-François Alcover_, Feb 20 2013 *)
%t RealDigits[-NIntegrate[Sin[Pi*x] Log[x]/x,{x,0,1}, WorkingPrecision-> 120],10,120][[1]] (* _Harvey P. Dale_, Oct 09 2017 *)
%K cons,easy,nonn
%O 1,1
%A _R. J. Mathar_, Mar 24 2010
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