Formula_21276

\[\begin{gathered}P_{n}(x ; \alpha, \beta)=P_{n}^{(\alpha, \beta)}(x)= \\=\frac{(-1)^{n}}{n ! 2 n}(1-x)^{-\alpha}(1+x)^{-\beta} \frac{d^{n}}{d x^{n}}\left[(1-x)^{\alpha}(1+x)^{\beta}\left(1-x^{2}\right)^{n}\right],\end{gathered}\]