\[\left(\tfrac{1}{2}(1-x)\right)^{\frac{1}{2}\alpha+\frac{1}{4}}\left(\tfrac{1}{%
2}(1+x)\right)^{\frac{1}{2}\beta+\frac{1}{4}}|P^{(\alpha,\beta)}_{n}\left(x%
\right)|\leq\frac{\Gamma\left(\max(\alpha,\beta)+n+1\right)}{{\pi}^{\frac{1}{2%
}}n!\left(n+\tfrac{1}{2}(\alpha+\beta+1)\right)^{\max(\alpha,\beta)+\frac{1}{2%
}}},\]