Orthogonal polynomialsIn mathematics, a polynomial sequence pn(x) for n = 0, 1, 2, ... is said to be a sequence of orthogonal polynomials with respect to a "weight function" w when
By convention pn has degree n; and w should give rise to an inner product, being non-negative and not 0 (see orthogonal).
- 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].