Two functions f(x) and g(x) are orthogonal over the interval a<=x<=b with weighting function w(x) if 〈f(x)|g(x)〉 congruent integral_a^b f(x) g(x) w(x) d x = 0. If, in addition, integral_a^b [f(x)]^2 w(x) d x | = | 1 integral_a^b [g(x)]^2 w(x) d x | = | 1, the functions f(x) and g(x) are said to be orthonormal.

complete biorthogonal system | complete orthogonal system | orthogonal polynomials | orthonormal functions