# Question regarding the definition of the complex fourier series

1. Sep 23, 2008

### Narcol2000

Why is the complex fourier series expanded from $$+\infty$$ to $$-\infty$$.

Yet the regular fourier series from 0 to $$+\infty$$?

2. Sep 23, 2008

### HallsofIvy

Staff Emeritus
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.

3. Sep 23, 2008

### Narcol2000

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