A175294 Decimal expansion of the integral of cos(Pi*x)*log(x)/x from x=1 to infinity.

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, 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, 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

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

0.05762490298863188764...

Maple

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 ) ;

Mathematica

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 *)

Crossrefs

Sequence in context: A145577 A144478 A059249 * A196615 A374967 A305200

Adjacent sequences: A175291 A175292 A175293 * A175295 A175296 A175297

Keyword

cons,easy,nonn

Author

R. J. Mathar, Mar 24 2010

Status

approved