The Jacobi polynomials $P_n^{(\alpha,\beta)}$, $n\geq 0$, can be defined as the system of orthogonal polynomials with respect to the inner product
(3) such that $\deg P_n^{(\alpha,\beta)}=n$ and $P_n^{(\alpha,\beta)}(1) = \binom{n+\alpha}{n}$. Due to
(4) and
(2) we restrict to $\alpha < \beta$.