A175295 Decimal expansion of the integral of cos(Pi*x)*log(x)/x^2 from x=1 to infinity.

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, 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, 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

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

R. J. Mathar, Numerical evaluation of the oscillatory integral over exp(i*pi*x)*x^(1/x) between 1 and infinity, arXiv:0912.3844 [math.CA], 2009-2010, App. B.

Formula

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

Example

0.02991320398393497843930179...

Maple

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 ) ;

Mathematica

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 *)
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 *)

Crossrefs

Sequence in context: A104954 A244292 A011072 * A198141 A336043 A340723

Adjacent sequences: A175292 A175293 A175294 * A175296 A175297 A175298

Keyword

cons,easy,nonn

Author

R. J. Mathar, Mar 24 2010

Status

approved