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MathGroup Archive 2005

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Re: FourierTransform

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57667] Re: FourierTransform
  • From: "Peltio" <peltio at trilight.zone>
  • Date: Fri, 3 Jun 2005 05:34:23 -0400 (EDT)
  • References: <d7k36h$oi1$1@smc.vnet.net> <d7mjn3$bvd$1@smc.vnet.net>
  • Reply-to: "Peltio" <peltioNOSPAM at despammed.com.invalid>
  • Sender: owner-wri-mathgroup at wolfram.com

"dh" wrote


>Integrate[Exp[-I*w*t],{t,0,infinity}]
>or more accurate:
>Integrate[Exp[-I*w*t], {t, 0, Infinity}, Assumptions ->Element[w,Reals]]
>should fail to converge because the integrand is a unit vector whose
>phase changes with constant velocity (with the exception w=0). However,
>Mathematica happily gives the answer:
>-I/w

It looks as if Mathematica is computing a finite version of the integral

    Integrate[Exp[-I*w*t],{t,0,b}]

getting

    Exp[-I w b]/(-I w) - Exp[-I w 0]/(-I w)
    I/w (Exp[-I w b]-1)

and then fails to do the limit for b->Infinity, assuming that
    Exp[- Infinity * something else] is zero
Is this a bug of Integrate or Limit?

cheers,
Peltio
invalid address in reply to. ecc. ecc.



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