Sets of polynomials Pn(x) that satisfy an orthogonality relationship on an interval a<x<b with respect to some inner product, i.e.:

|  W(x)P (x)P (x) dx = 0, k ≠ n
/a      n    k
where W(x) is an arbitrary weight function. Most orthogonal polynomials have a representation in the form of a Rodrigues formula that involves differentiation, and obey a recurrence relation.

The most common orthogonal polynomials include the Legendre polynomials, Laguerre polynomials, Hermite polynomials, Chebyshev polynomials, Gegenbauer polynomials, and Jacobi polynomials.