Two functions 
and 
are orthogonal over the interval 
with weighting
function 
if
 |
(1)
|
If, in addition,
![int_a^b[f(x)]^2w(x)dx](/images/equations/OrthogonalFunctions/Inline5.svg) |  |  |
(2)
|
![int_a^b[g(x)]^2w(x)dx](/images/equations/OrthogonalFunctions/Inline8.svg) |  |  |
(3)
|
the functions 
and 
are said to be orthonormal.
Orthogonal Functions
See also
Complete Biorthogonal System, Complete Orthogonal System, Complete Set of Functions, Orthogonal Polynomials, Orthonormal FunctionsExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Orthogonal Functions." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OrthogonalFunctions.html