Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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