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

/b
| 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.