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Re: Fourier Transforms


On Mar 2, 2006, at 6:48 AM, Ben C wrote:

> On the first of March I posted an appeal for help with some Fourier
> transforms. Since then a couple of people have suggested I post the
> actual transforms. I am trying to inverse Fourier transform the
> functions
>
> p / (sqrt(1+p^2 + sqrt(1+p^2 ))   and   1/(sqrt(1+p^2 - sqrt(1+p^2 ))
>
> from p to x space.
>
> Any advice would again be extremely gratefully received,

You need to convert your expressions to proper Mathematica syntax,  
sqrt(x) is Sqrt[x] in Mathematica.  Since you're looking for a  
symbolic solution use InverseFourierTransform like so:

In[3]:=
InverseFourierTransform[p/Sqrt[1+p^2+Sqrt[1+p^2]],p,x]
InverseFourierTransform[1/Sqrt[1+p^2-Sqrt[1+p^2]],p,x]
Out[3]=
0
Out[4]=
InverseFourierTransform[1/Sqrt[1+p^2-Sqrt[1+p^2]], p, x]

The second expression returns itself because the integral cannot be  
performed.  Perhaps your expression is only valid for p > 0?  You  
also need to specify the convention for the Fourier transform you are  
using, see the Help Browser for more information.

Regards,

Ssezi


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