# Fourier Series coefficients, orthogonal?

1. Oct 19, 2011

### Dollydaggerxo

1. The problem statement, all variables and given/known data

Hello. I need help with orthogonality of the fourier series coefficients. I know you can use the dirac delta function, (or the kronecker function) in the orthogonality relationship. I want to try and see the derivation using complex form rather than sines and cosines.

2. Relevant equations

proof of
$\frac{1}{T}\int^T_0 e^{inw_0t}e^{-imw_0t} dt = \delta_{m}{n}$

3. The attempt at a solution

Basically I havent got very far, do not know where to start in this proof. any help would be appreciated?

thanks

2. Oct 19, 2011

### susskind_leon

Obviously, m and n must be integers, which makes things really easy. Just assume m=n, do the integration and write down what you get. Then assume $m \neq n$, do the integration and write down what you get.

3. Oct 19, 2011

### Dollydaggerxo

Okay I have got it. Thanks!

Last edited: Oct 19, 2011