find Fourier transform on this given function the function is: $f(x)=e^{-\alpha x^2} , \alpha > 0$

Asked May 23 '21 at 05:54

Active May 23 '21 at 06:12

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im working on a PDE question.

which states : find Fourier transform on this given function the function is: $$f(x)=e^{-\alpha x^2} , \alpha > 0$$

we know that for Fourier transform : $$F(w)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty} f(x) e^{-iwx} dx$$

so $$F(w)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty} e^{-\alpha x^2} e^{-iwx} dx$$

how should I solve this ?

I tried to simplify it but it just got more complicated.

edited May 23 '21 at 06:12

asked May 23 '21 at 05:54

Noah

2

Hint: calculate $F'(\omega)$ and try to write it in terms of $F(\omega)$. – Bobo May 23 '21 at 06:01
@Bobo doesnt this make it more complicated than simplify it ? – Noah May 23 '21 at 06:19

0 Answers0