\[\rho_{j}(f_{0}+2\rho_{j})sa_{s,j}=\sum_{r=1}^{s}\left(\rho_{j}^{2}2^{r+1}%
\genfrac{(}{)}{0.0pt}{}{\alpha_{j}+r-s}{r+1}+\rho_{j}\sum_{q=0}^{r+1}\genfrac{%
(}{)}{0.0pt}{}{\alpha_{j}+r-s}{r+1-q}f_{q}+g_{r+1}\right)a_{s-r,j},\]