  \begin{equation}
    \begin{gathered}
    R_1 = \frac{(s + 1)^{\frac{1}{\alpha}}f_0}{
      \alpha^4(s + 1)^2(s + \alpha - 1)} \\
    \text{ with } f_0 = 
      2(1 - \alpha)s^3
        + (\alpha^3 - 4\alpha^2 + 9\alpha - 6)s^2
        + (\alpha^3 + 6\alpha^2 - 12\alpha + 6)s\\
        + (\alpha^4 - \alpha^3 - 2\alpha^2 + 5\alpha - 2),\\
    R_{23} = \frac{(s + 1)^{\frac{1}{\alpha}}((2\alpha - 1)s + \alpha^2 - \alpha + 1)}{\alpha^2(s + 1)^2(s + \alpha - 1)}, \\    
    R_4 = \frac{(s+\alpha)(s + 1)^{\frac{1}{\alpha}}}{\alpha(s + 1)^2(s+\alpha-1)}.
    \end{gathered}
\end{equation}    
