\[\operatorname{Disc}\left(P^{(\alpha,\beta)}_{n}\right)=2^{-n(n-1)}\prod_{j=1}^%
{n}j^{j-2n+2}(j+\alpha)^{j-1}(j+\beta)^{j-1}(n+j+\alpha+\beta)^{n-j}.\]