NC n^(lambda)(x)=(n-1+2lambda)xC (n-1)^(lambda)(x)-2lambda(1-x^2)C (n-2)^(lambda-1)(x)
From specialfunctionswiki
Theorem
The following formula holds: $$nC_n^{\lambda}(x) = (n-1+2\lambda)xC_{n-1}^{\lambda}(x) - 2\lambda(1-x^2)C_{n-2}^{\lambda-1}(x),$$ where $C_n^{\lambda}$ denotes Gegenbauer C.
