這函數的傅立葉展開式為

 證明:

                       

                           

                           

                     

                         

                         

                       當 

                       當 

                       當 

                       當 

                        當

                      

                           

                          

                    

                           

                                   

                         

 

     n=0時,

傅立葉級數動畫

    n=1時,

傅立葉級數動畫

 

    n=3時,

傅立葉級數動畫

 

應用

          令 得到