\[\sum_{m=0}^{n}\frac{{\left(\lambda+1\right)_{n-m}}}{(n-m)!}\frac{{\left(%
\lambda+1\right)_{m}}}{m!}\mbox{$\displaystyle\frac{P^{(\alpha,\beta)}_{m}%
\left(x\right)}{P^{(\beta,\alpha)}_{m}\left(1\right)}\geq 0$},\]