Racah polynomials

Summary

The Racah polynomials are a finite family of orthogonal polynomials, given by terminating balanced ${}_4F_3$ hypergeometric series. They are polynomials in the quadratic variable $\lambda(x) = x(x + \gamma + \delta + 1)$, orthogonal for a weight on the points $x = 0, 1, \dots, N$. They sit at the top of the Askey scheme together with the Wilson polynomials. They are named after Giulio Racah because the 6-j symbols of quantum angular momentum can be written in terms of them.