Find the \(z\)-transforms of the following functions:

(a) \(E(s)=\frac{\varepsilon^{3}-1}{\varepsilon^{3} s(s+1)}, \quad T=0.2 \mathrm{~s}\)

(b) \(E(s)=\frac{(0.8 s+1)\left(1-\varepsilon^{0.5} sight)}{0.8 s(s+0.5)}, \quad T=0.5 \mathrm{~s}\)