\[{{}_{1}F_{1}}\left({-x\atop\alpha+1};-z\right){{}_{1}F_{1}}\left({x-N\atop%
\beta+1};z\right)=\sum_{n=0}^{N}\frac{{\left(-N\right)_{n}}}{{\left(\beta+1%
\right)_{n}}n!}Q_{n}\left(x;\alpha,\beta,N\right)z^{n},\]