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