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Question regarding the definition of the complex fourier series

  1. Sep 23, 2008 #1
    Why is the complex fourier series expanded from [tex]+\infty[/tex] to [tex]-\infty[/tex].

    Yet the regular fourier series from 0 to [tex]+\infty[/tex]?
     
  2. jcsd
  3. Sep 23, 2008 #2

    HallsofIvy

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    einx= cos(nx)+ i sin(nx). cos(x) is an even function while sin(x) is an odd function: cos(-nx)= cos(nx), sin(-nx)= -sin(nx). Negative values of n are alread "incorporated" into the coefficients. ei(-n)x= cos(-nx)+ isin(-nx)= cos(nx)- i sin(nx) so changing n for -n in the complex exponential gives the complex conjugate.
     
  4. Sep 23, 2008 #3
    Ah i see that explans the difference of a factor of two between the regular coefficients and complex coefficients...

    thanks
     
    Last edited: Sep 23, 2008
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