Complex form of Fourier series

1. Jul 5, 2010

roshan2004

Though I can compute the coefficients of Trigonometric form of Fourier series, how can I compute the coefficients of complex form of Fourier series.

2. Jul 5, 2010

nekronaut

I assume you mean on the form e^ix? Or am I on the wrong track here?

If my assumption is correct you want to write your function on the form
$$f(x) = \sum_{-\infty}^{\infty}c_ke^{inx}$$

If so, the Fourier coefficents are given by

$$c_k = \frac{1}{2\pi}\int_{-\pi}^{\pi}f(x)e^{-inx}$$

3. Jul 5, 2010

mathman

Since you know how to compute Fourier series using sine and cosine, just use the identity:
e-inx=cos(nx)-isin(nx).

4. Jul 5, 2010

roshan2004

Have you guys got any links where there is proof of derivation of complex fourier series?