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Re: Calculation of a not so simple integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg131224] Re: Calculation of a not so simple integral
  • From: "Dr. Wolfgang Hintze" <weh at snafu.de>
  • Date: Wed, 19 Jun 2013 01:26:09 -0400 (EDT)
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Alexei,
you might have missed the extensive discussion on this integral some
days ago
https://groups.google.com/group/comp.soft-sys.math.mathematica/browse_thread/thread/960f9facb5a3683b?hl=de#
Best regards,
Wolfgang

On 17 Jun., 12:19, Alexei Boulbitch <Alexei.Boulbi... at iee.lu> wrote:
> (*Partial Fractions decomposition,  Fourier Integrals
>
> The problem diagnostics:
>
> Calculate
>
> Integrate[ Sin[x/2]^2 / x^2 / (x^2-4*Pi^2 )^2 / (x^2 + a^2)^2 ,
> {x,-oo,oo}, Assumptions-> a>0]
>
> The integrand is nonnegative, has no poles on the real line and decays
> rapidly  ~ x^-10 as x->+-oo
>
> Hi, Roland,
>
> I checked your expression, it has a pole on the x axis. Check this
>
> Sin[x/2]^2 / x^2 / (x^2-4*Pi^2 )^2 / (x^2 + a^2)^2//StandardForm
>
> Could it be the case, that you have just written it down in a wrong way?
>
> Alexei BOULBITCH, Dr., habil.
> IEE S.A.
> ZAE Weiergewan,
> 11, rue Edmond Reuter,
> L-5326 Contern, LUXEMBOURG
>
> Office phone :  +352-2454-2566
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>
> e-mail: alexei.boulbi... at iee.lu




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