Hahn polynomials

Summary

The Hahn polynomials $Q_n(x; \alpha, \beta, N)$ are a finite family of orthogonal polynomials on the points $0, 1, \dots, N$. Their weight is the beta-binomial distribution, a discrete version of the Jacobi weight. They are terminating ${}_3F_2$ hypergeometric series and sit in the Askey scheme just below the Wilson and Racah polynomials. As $N \to \infty$ after rescaling they tend to the Jacobi polynomials, and they also appear as Clebsch–Gordan coefficients of $SU(2)$.