Re: Calculation of a not so simple integral

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• Subject: [mg131221] Re: Calculation of a not so simple integral
• From: "Brambilla Roberto Luigi (RSE)" <Roberto.Brambilla at rse-web.it>
• Date: Wed, 19 Jun 2013 01:25:09 -0400 (EDT)
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```The integrand has NO poles on the real axis : in x=+/-(2*Pi) the integrand assume zero value :

Limit[Sin[x/2]^2/(x^2 - 4 Pi^2), x -> 2 Pi]
0

Rob.

-----Messaggio originale-----
Da: Alexei Boulbitch [mailto:Alexei.Boulbitch at iee.lu]
Inviato: luned=EC 17 giugno 2013 12.32
A: mathgroup at smc.vnet.net
Oggetto: Re: Calculation of a not so simple integral

(*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.
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