A generalized Fourier series is a series expansion of a function based on the special properties of a complete orthogonal system of functions. The prototypical example of such a series is the Fourier series, which is based of the biorthogonality of the functions cos(n x) and sin(n x) (which form a complete biorthogonal system under integration over the range [-π, π]). Another common example is the Laplace series, which is a double series expansion based on the orthogonality of the spherical harmonics Y_l^m(θ, ϕ) over θ element [0, π] and ϕ element [0, 2π].

Bessel function Neumann series | Bessel's inequality | Fourier-Bessel series | Fourier-Legendre series | Fourier series | generalized Fourier integral | Kapteyn series | Laplace series | orthogonal basis | orthogonal polynomials | orthonormal basis | Parseval's theorem