\[P^{(\alpha,\beta)}_{n}\left(x\right)=2^{-n}\sum_{\ell=0}^{n}\genfrac{(}{)}{0.0%
pt}{}{n+\alpha}{\ell}\genfrac{(}{)}{0.0pt}{}{n+\beta}{n-\ell}(x-1)^{n-\ell}(x+%
1)^{\ell}=\frac{{\left(\alpha+1\right)_{n}}}{n!}\left(\frac{x+1}{2}\right)^{n}%
{{}_{2}F_{1}}\left({-n,-n-\beta\atop\alpha+1};\frac{x-1}{x+1}\right),\]