Orthogonal functions

In mathematics, two functions $f$ and $g$ are orthogonal if their inner product $\langle f,g\rangle$ is zero. Whether or not two particular functions are orthogonal depends on how their inner product has been defined. A typical definition of an inner product for functions is

$\langle f(x),g(x)\rangle =\int f^{*}(x)g(x)dx,$

with appropriate integration boundaries. See further Hilbert space for more background.