\[C^{(\lambda)}_{2n+1}\left(x\right)=\frac{{\left(\lambda\right)_{n+1}}}{{\left(%
\frac{1}{2}\right)_{n+1}}}xP^{(\lambda-\frac{1}{2},\frac{1}{2})}_{n}\left(2x^{%
2}-1\right).\]