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