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In the first integral f(x) has been changed into its complex conjugate. |
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In [[mathematics]], '''orthogonal functions''' belong to a [[function space]] which is a [[vector space]] (usually over R) that has a [[bilinear form]]. When the function space has an [[interval (mathematics)|interval]] as the [[___domain of a function|___domain]], the bilinear form may be the [[integral]] of the product of functions over the interval:
:<math> \langle f,g\rangle = \int \overline{f(x)}g(x)\,dx .</math>
The functions ''f'' and ''g'' are [[bilinear form#Reflexivity and orthogonality|orthogonal]] when this integral is zero: <math>\langle f, \ g \rangle = 0.</math>
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