\[P\begin{Bmatrix}\alpha&\beta&\gamma&\\
a_{1}&b_{1}&c_{1}&z\\
a_{2}&b_{2}&c_{2}&\end{Bmatrix}=\left(\frac{z-\alpha}{z-\gamma}\right)^{a_{1}}%
\left(\frac{z-\beta}{z-\gamma}\right)^{b_{1}}P\begin{Bmatrix}0&1&\infty&\\
0&0&a_{1}+b_{1}+c_{1}&\dfrac{(z-\alpha)(\beta-\gamma)}{(z-\gamma)(\beta-\alpha%
)}\\
a_{2}-a_{1}&b_{2}-b_{1}&a_{1}+b_{1}+c_{2}&\end{Bmatrix}.\]