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