\[P^{{(\lambda)}}_{n+1}\left(x;a,b,c\right)=\frac{2(n+c+\lambda+a)x+2b}{n+c+1}\,%
P^{{(\lambda)}}_{n}\left(x;a,b,c\right)-\frac{n+c+2\lambda-1}{n+c+1}\,P^{{(%
\lambda)}}_{n-1}\left(x;a,b,c\right),\]