\[C^{(0)}_{n}\left(x\right)=\frac{2}{n}T_{n}\left(x\right)=\frac{2(n-1)!}{{\left%
(\tfrac{1}{2}\right)_{n}}}P^{(-\frac{1}{2},-\frac{1}{2})}_{n}\left(x\right),\]