Could anyone give me a suggestion to calculate the Fourier transform of the following function?
$f:\mathbb{R}\to\mathbb{C}$ defined by $\displaystyle{f(x) = \frac{1}{(x+i)^{n}}} $
where $n$ is a integer and $n\geqslant{2}$
2026-04-06 00:42:30.1775436150
Fourier transform of $\displaystyle{f(x) = \frac{1}{(x+i)^{n}}} $
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HINT:
$$F(k)=\int_{-\infty}^\infty \frac{e^{ikx}}{x+i}\,dx=\begin{cases}0&,k>0\\\\-2\pi ie^{-|k|} &,k<0\end{cases}$$
What is $F'(k)$? What is $F''(k)$? What is $F^{(n)}(k)$?