函数若在区间(a,b)可积，且，则可作为权函数。

对于一个多项式的串行和权函数，定义内积

若，，这些多项式则称为正交多项式。

若除了正交之外，更有的话，则称为规范正交多项式。

若权函数为1，区间为(-1,1)，，对应的正交多项式有：

它们称为勒让德多项式。

对于任意矢量空间的基，Gram-Schmidt正交化可以求出一个正交基。对于多项式空间的基，正交化的结果便是勒让德多项式。

In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product.

The most widely used orthogonal polynomials are the classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials, the Jacobi polynomials together with their special cases the Gegenbauer polynomials, the Chebyshev polynomials, and the Legendre polynomials.