A175296 Decimal expansion of the absolute value of the integral of sin(Pi*x)*log(x)/x^2 from x=1 to infinity.

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, 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, 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

Offset

0,2

Links

Table of n, a(n) for n=0..104.

R. J. Mathar, Numerical evaluation of the oscillatory integral..., arXiv:0912.3844 [math.CA], App. B.

Example

0.050400599397438879223...

Maple

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 ) ;

Mathematica

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 *)

Crossrefs

Sequence in context: A202626 A011995 A258754 * A076266 A350281 A354053

Adjacent sequences: A175293 A175294 A175295 * A175297 A175298 A175299

Keyword

cons,easy,nonn

Author

R. J. Mathar, Mar 24 2010

Status

approved