A175295 - OEIS

%I #12 Sep 07 2018 04:42:55

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

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

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

%N Decimal expansion of the integral of cos(Pi*x)*log(x)/x^2 from x=1 to infinity.

%H G. C. Greubel, <a href="/A175295/b175295.txt">Table of n, a(n) for n = 0..10000</a>

%H R. J. Mathar, <a href="http://arxiv.org/abs/0912.3844">Numerical evaluation of the oscillatory integral over exp(i*pi*x)*x^(1/x) between 1 and infinity</a>, arXiv:0912.3844 [math.CA], 2009-2010, App. B.

%F 1+ A102753*( A053510 -1 + A001620 - 3F4(1/2,1/2,1; 3/2,3/2,3/2,2 ; -A091476) ) .

%e 0.02991320398393497843930179...

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

%t Join[{0}, RealDigits[ N[1/2*(Pi^2*(-2*HypergeometricPFQ[{1/2, 1/2}, {3/2, 3/2, 3/2}, -Pi^2/4] + Log[Pi] + EulerGamma - 1) + 2*Pi*SinIntegral[Pi] - 2), 105]][[1]]] (* _Jean-François Alcover_, Nov 08 2012 *)

%t Join[{0},RealDigits[NIntegrate[Cos[Pi*x] Log[x]/x^2,{x,1,\[Infinity]}, WorkingPrecision->1000],10,120][[1]]] (* _Harvey P. Dale_, Nov 01 2017 *)

%K cons,easy,nonn

%O 0,2

%A _R. J. Mathar_, Mar 24 2010