MathGroup Archive 2010

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: integrate log*sinc


On Apr 16, 4:52 am, pimeja <sed.n... at gmail.com> wrote:
> Hi All,
>
> For Integrate[Log[x] Sin[x]/x, {x, 0, \[Infinity]}] Mathematica
> returns -EulerGamma \[Pi].
> How to proof this analytical?

In[8]:= Limit[D[Integrate[x^(s - 1)*Sin[x], {x, 0, Infinity},
       Assumptions -> -1 < s < 1], s], s -> 0]

Out[8]= -((EulerGamma*Pi)/2)

>
> I've tried to use residue theory but it seems not suitable since
> integrand has pool of second order in zero (for Jordan lema should be
> first order only). Substitution x=Exp[y] returns even more strange
> result.
>
> Thanks in advance.



  • Prev by Date: Re: How to make style sheet with header
  • Next by Date: Re: How to simplify "Integrate[2 f[x], {x, 0, 1}]/2" to "Integrate[f[x],
  • Previous by thread: integrate log*sinc
  • Next by thread: Re: integrate log*sinc