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