# Complex fourier series

• July 6th 2010, 02:22 PM
roshanhero
Complex fourier series
While deriving complex fourier series I have reached at $c_0+\sum_{n=1}^{n=\infty}c_ne^{\frac{in\pi x}{l}}+\sum_{n=-1}^{n=-\infty}c_ne^\frac{in\pi x}{l}$.
Can anyone tell me what combined expression (pattern) can be written for this and why?
• July 6th 2010, 03:02 PM
Jester
You notice that when $n = 0$ then $c_n e^{\frac{i n \pi x}{L}}= c_0$ so your entire sum can be written as

so $\sum \limits_{n = -\infty}^{-1} c_n e^{\frac{i n \pi x}{L}} + c_0 + \sum \limits_{n = 1}^{\infty} c_n e^{\frac{i n \pi x}{L}} = \sum \limits_{n = -\infty}^{\infty} c_n e^{\frac{i n \pi x}{L}}$