\[L^{(\alpha_{1}+\dots+\alpha_{r}+r-1)}_{n}\left(x_{1}+\dots+x_{r}\right)=\sum_{%
m_{1}+\dots+m_{r}=n}L^{(\alpha_{1})}_{m_{1}}\left(x_{1}\right)\cdots L^{(%
\alpha_{r})}_{m_{r}}\left(x_{r}\right).\]