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Re: Why the FourierTransform gives two different answers?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg125138] Re: Why the FourierTransform gives two different answers?
  • From: Dana DeLouis <dana.del at gmail.com>
  • Date: Thu, 23 Feb 2012 05:49:31 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

> Why the FourierTransform gives two different answers?

> In[1]     FourierTransform[ (t - 5.0)^2*Exp[-(t - 5.0)^2 ], t, w]
> In[2]     FourierTransform[ (t - 5)^2*  Exp[-(t - 5)^2 ], t, w]


Hi.  I don't have an answer, but an observation.
This seems strange, and I don't really see where the machine rounding 
error is coming from.
If we take a basic formula of the Fourier equation, then the question is 
why is the first part dropped to zero when done at machine precision.

FullSimplify[Integrate[(t - 5)^2*Exp[-(t - 5)^2], t]]

((-(1/2))*(-5 + t))/E^(-5 + t)^2 - (1/4)*Sqrt[Pi]*Erf[5 - t]

FullSimplify[Integrate[(t - 5.)^2*Exp[-(t - 5.)^2], t]]

0. - 0.44311346272637897*Erf[5. - 1.*t]

The difference is this part...

equ=-(1/2) E^-(-5+t)^2 (-5+t);

It plots nicely:
Plot[equ,{t,0,5}]

It has a nice value at 4:

N[equ]   /.t->4
0.18394

But for some reason, simplifying it gives 0.

N[equ]   //FullSimplify
0.

I don't have an explanation for this behavior  (bug maybe??)

Even if we substitute w for t-5, it still doesn't reduce to zero at full 
precision, and it does plot nicely.

FullSimplify[((-(1/2))*w)/E^w^2]
((-(1/2))*w)/E^w^2

= = = = = = = = = = = = = = =
HTH  :>)
Dana DeLouis
Mac & Math 8
= = = = = = = = = = = = = = =


On Feb 21, 6:22 am, =D0=90=D0=BB=D0=B5=D0=BA=D1=81=D0=B5=D0=B9 <avde... at gmail.com> wrote:
> Why the FourierTransform gives two different answers?
>
> In[1]     FourierTransform[ (t - 5.0)^2*Exp[-(t - 5.0)^2 ], t, w]
>
> In[2]     FourierTransform[ (t - 5)^2*  Exp[-(t - 5)^2 ], t, w]





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