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The Fourier transform of

\[x(t)=\frac{t^{n-1}}{(n-1) !} \mathrm{e}^{-a t} u(t), \quad a>0\]

$(\jmath=\sqrt{-1}, u(t)=1$ for $t \geq 0, u(t)=0, t<0)$ is

  1. $(a+\jmath \omega)^{n}$
  2. $\sum_{k=1}^{n} \frac{(a+\jmath \omega)^{k}}{k !}$
  3. $na\jmath \omega$
  4. $\frac{1}{(a+\jmath \omega)^{n}}$
  5. None of the above.
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