\[\frac{\mathrm{d}}{\mathrm{d}x}\left((1-x^{2})^{\lambda-\frac{1}{2}}C^{(\lambda%
)}_{n}\left(x\right)\right)=-\frac{(n+1)(n+2\lambda-1)}{2(\lambda-1)}{(1-x^{2}%
)^{\lambda-\frac{3}{2}}}C^{(\lambda-1)}_{n+1}\left(x\right).\]