A175296 - OEIS

%I #5 Nov 08 2012 02:35:32

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

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

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

%N Decimal expansion of the absolute value of the integral of sin(Pi*x)*log(x)/x^2 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 0.050400599397438879223...

%p evalf(Pi*(-Pi^2/24+gamma*( gamma/2+log(Pi)-1 )+log(Pi)*( log(Pi)/2-1)+1 ) -Pi^3* hypergeom([1,1,1],[2,2,2,5/2],-Pi^2/4)/24 ) ;

%t Join[{0}, RealDigits[N[-1/24*Pi* (Pi^2*(HypergeometricPFQ[{1, 1, 1}, {2, 2, 2, 5/2}, -Pi^2/4] + 1) + 24*(Log[Pi] - 1) - 12*(Log[Pi]^2 + EulerGamma^2 + 2*EulerGamma*(Log[Pi] - 1))), 105]][[1]]] (* _Jean-François Alcover_, Nov 08 2012 *)

%K cons,easy,nonn

%O 0,2

%A _R. J. Mathar_, Mar 24 2010