complete functions

A set of functions {f_1(n, x), f_2(n, x)} is termed a complete biorthogonal system in the closed interval R if, they are biorthogonal, i.e., integral_R f_1(m, x) f_1(n, x) d x | = | c_m δ_(m n) integral_R f_2(m, x) f_2(n, x) d x | = | d_m δ_(m n) integral_R f_1(m, x) f_2(n, x) d x | = | 0 integral_R f_1(m, x) d x | = | 0 integral_R f_2(m, x) d x | = | 0 and complete.

complete orthogonal system | Fourier series | generalized Fourier series