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%I #5 Nov 08 2012 02:36:37
%S 0,5,7,6,2,4,9,0,2,9,8,8,6,3,1,8,8,7,6,4,3,4,8,5,5,4,2,2,3,9,9,0,2,8,
%T 0,3,6,5,3,5,1,6,2,4,5,9,4,3,3,8,1,4,8,6,0,5,5,4,9,4,6,2,2,7,9,8,8,3,
%U 3,6,5,5,1,3,9,3,8,8,5,3,0,6,0,1,0,9,9,7,9,3,3,0,1,6,8,5,0,2,7,2,5,3,5,8,1
%N Decimal expansion of the integral of cos(Pi*x)*log(x)/x from x=1 to infinity.
%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 0.05762490298863188764...
%p evalf(-Pi^2/24+gamma*(gamma/2+log(Pi))+log(Pi)^2/2 -Pi^2*hypergeom([1,1,1],[3/2,2,2,2],-Pi^2/4)/8 ) ;
%t Join[{0}, RealDigits[N[1/24*(12*(Log[Pi] + EulerGamma)^2 - Pi^2*(3*HypergeometricPFQ[{1, 1, 1}, {3/2, 2, 2, 2}, -Pi^2/4] + 1)), 105]][[1]]] (* _Jean-François Alcover_, Nov 08 2012 *)
%K cons,easy,nonn
%O 0,2
%A _R. J. Mathar_, Mar 24 2010
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