# I Q about Fourier Coefficient Derivation

1. Mar 30, 2016

### Enigma322

For the calculation of cn u have to multiply the equation

∑ cn * ejnx
by
e-jmx

what is the reason for this? in my textbook it says nothing about it and on some sites it just said "without justification"
i guess what im asking is why does this do what we want?
ps: how do u properly make equations here?

2. Mar 30, 2016

### blue_leaf77

It's not just multiplication, but you also have to integrate the resulting product function. It's done this way because
$$\int_{0}^L \exp\left(\frac{2\pi}{L}(m-n)u\right) du \propto \delta_{mn}$$

3. Mar 30, 2016

### Ssnow

Yes, the elements $\{e^{jnx}\}$ form an orthonormal system on your Hilbert space ...