Orthonormal Functions

A pair of functions $\phi_i$ and $\phi_j$ are orthonormal if they are Orthogonal and each normalized. These two conditions can be succinctly written as

$$\int^b_a \phi_i(x)\phi_j(x)w(x)\,dx = \delta_{ij},$$

where $w(x)$ is a Weighting Function and $\delta_{ij}$ is the Kronecker Delta.

See also Orthogonal Polynomials