Re: InverseFourierTransform strange behaviour

• To: mathgroup at smc.vnet.net
• Subject: [mg82323] Re: InverseFourierTransform strange behaviour
• From: roby.nowak at gmail.com
• Date: Wed, 17 Oct 2007 04:13:05 -0400 (EDT)
• References: <fesjid\$ks8\$1@smc.vnet.net><ff1qf0\$9ao\$1@smc.vnet.net>

```Hi Frank,

sorry but you are not correct.

2 Sqrt[2/Pi] Exp[(w/2)^2] Sin[w]/w
is pefectly even (as it is without the negative sign as you suggested)

Exp[(w/2)^2]  is even
Sin[w]           is odd
1/w               is odd
Sin[w]/w        is even

a simple numerical test too shows that the function is even ( f[x] ==
f[-x] )

@everybody

I am in doubt now if the IFT exists for my function. any suggestions
to this ?

regards robert

On 16 Okt., 09:49, Frank Iannarilli <frank... at cox.net> wrote:
> On Oct 14, 4:21 am, roby.no... at gmail.com wrote:
>
> > In[1]:= 2 Sqrt[2/Pi] Exp[(w/2)^2] Sin[w]/w;
> > InverseFourierTransform[%, w, x]
>
> Your function is actually not even, but I believe you intended it to
> be:
>   2 Sqrt[2/Pi] Exp[-(w/2)^2] Sin[w]/w
>                         ^^^^
>                  (note inserted negative sign)
>
> In this case, everything will work as you expected.
>
> Regards,

```

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