Applied Mathematics/Fourier Series

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IntroductionEdit

For the function  , Taylor expansion is possible.

 

This is the Taylor expansion of  . On the other hand, more generally speaking,   can be expanded by also Orthogonal f

Fourier seriesEdit

For the function   which has   for its period, the series below is defined:

 

This series is referred to as Fourier series of  .   and   are called Fourier coefficients.

 
 

where   is natural number. Especially when the Fourier series is equal to the  , (1) is called Fourier series expansion of  . Thus Fourier series expansion is defined as follows: