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.