Definition  
For a periodic function with fundamental period , the corresponding Fourier Series representation is given by: The Fourier Coefficients and can be determined from the following integrals: where can be interpreted as the average value of over the interval . Also Note that the above integration interval from  to can actually be any interval of length , such as from 0 to , which may be more convenient in some cases.
 
Important: For nonperiodic functions, one can argue that they are periodic with an infinite period, that is, . The Fourier Series then becomes the Fourier Integral. 
Complex Form of Fourier Series 
If one uses the complex forms
of and , the
Fourier Series of function becomes: where: 
Fourier Series of Selected Functions  
