\[4\lambda(n+\lambda+1)(1-x^{2})C^{(\lambda+1)}_{n}\left(x\right)=-(n+1)(n+2)C^{%
(\lambda)}_{n+2}\left(x\right)+(n+2\lambda)(n+2\lambda+1)C^{(\lambda)}_{n}%
\left(x\right).\]