**By convention p_{n} has degree n; and w should give rise to an inner product, being non-negative and not 0 (see orthogonal).**

For example:

- The Hermite polynomials are orthogonal with respect to a normal probability distribution.
- The Chebyshev polynomials are orthogonal with respect to the weight function

- The Legendre polynomials are orthogonal with respect to the uniform probability distribution on the interval [−1, 1].