# Fourier Series Notation

Can fourier series notation be written in different ways but get the same result? I ask because I've seen these two diferent notations. What is the difference between the two? If they produce the same result I will just keep using the first one, as I am more comfertable with it. Thanks :)

and this notation:

• They're largely just different notations for the same thing. But there is one key difference: In the first one, the domain of periodicity is $[-L,L]$ whereas in the latter it's $[0,T]$. So you shouldn't expect to get identical results. – Semiclassical Jun 16 '16 at 19:07
• Frankly, I see no significant differences between the two. You should be able to abstract away from the naming/particular definition of the constants and similar details. Ad be ready to handle yet other notations. – Yves Daoust Jun 16 '16 at 19:07
• Yeah, I thought they were very similar, except for the domains. The only things I wasn't really sure about were the a_0/2 coefficient at the start and the kwt and how that compares to (npix)/L – says Jun 16 '16 at 19:11

$$k\omega t = \frac{2\pi kt} T \quad\text{if} \quad \omega = \frac{2\pi} T \quad \text{or} \quad T=\frac{2\pi} \omega.$$