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Find the Fourier tranform of $f(x)=x^2e^{-x^2}$

In a previous question when I found the Fourier transform of $f(x) =e^{-x^2}$, I used the formulas $F(f')=i\omega F$ and $F(xf)=iF'$. Will they be helpful in this case?

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Consider applying the formula $\widehat{(xf)}(\omega)=i\frac{d}{d\omega}\widehat{f}(\omega)$ twice...

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Thankyou @anon .. I will try to do it – Hala Shubair Apr 28 '12 at 9:06

Hint: Wikipedia should be very helpful for this :

  • look at the top of the table and find your definition of Fourier transform
  • search the useful formula : $x^n f(x)$ here
  • apply to $f(x)=e^{-x^2}$

Fine continuation,

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Thankyou @Raymond Manzoni that was helpful – Hala Shubair Apr 28 '12 at 9:06

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