# §32.15 Orthogonal Polynomials

Let , , be the orthonormal set of polynomials defined by

with recurrence relation

32.15.2

for ; compare §18.2. Then satisfies the nonlinear recurrence relation

32.15.3

for , and also  with and .

For this result and applications see Fokas et al. (1991): in this reference, on the right-hand side of Eq. (1.10), should be replaced by at its first appearance. See also Freud (1976), Brézin et al. (1978), Fokas et al. (1992), and Magnus (1995).