\[C^{(\lambda)}_{n}\left(\cos\theta\right)=\sum_{\ell=0}^{n}\frac{{\left(\lambda%
\right)_{\ell}}{\left(\lambda\right)_{n-\ell}}}{\ell!\;(n-\ell)!}\cos\left((n-%
2\ell)\theta\right)={\mathrm{e}}^{\mathrm{i}n\theta}\frac{{\left(\lambda\right%
)_{n}}}{n!}{{}_{2}F_{1}}\left({-n,\lambda\atop 1-\lambda-n};{\mathrm{e}}^{-2%
\mathrm{i}\theta}\right).\]