Askey scheme

Summary

The Askey scheme is a chart that organises the hypergeometric orthogonal polynomials into levels connected by limit relations. At the top are the Wilson and Racah polynomials, given by ${}_4F_3$ series; at the bottom are the Hermite polynomials. Each arrow says that one family is a limit of another as a parameter tends to a special value or to infinity. It shows the classical families of Jacobi, Laguerre and Hermite as degenerations of a few very general ones.