FOURIER SERIES

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                               FOURIER SERIES

A Fourier series is defined as an expansion of periodic function or represent in a series of sines and cosines



     

where



 Function must satisfy the Dirichlet condition.

The fourier series expansion in the interval -L to L is given by



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                 Half-Range Fourier Series                                                  A Fourier series for f (x) , valid on [0, L], may be constructed by extension of the domain to [−L, L].

  An odd extension leads Fourier sine series:



  An even extension leads Fourier cosine series:

 





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