Even and odd extensions of a function

Can we find the Fourier series of a function which is only given between 0 and L? For a Fourier series we need a periodic function,
given between say -L and L and then continued periodically with period 2L.
If our function is only specified between 0 and L, we first need to define a new function, which is the original function from 0 to L and something else from -L to 0. We can tend extend this new function periodically and determine the fourier series of this new function.

This series will depend on the choice we made in the first step; so we will get different fourier series. However between 0 and L all these series will converge to our original function f(x). So how do we make this choice? In this video you will see two common extensions, the even and odd extensions and you will learn why these extensions are often used.

[kwanele]

Very brief yet straightforward explanation. I needed that 🙌🙌