- #1
Niles
- 1,866
- 0
Homework Statement
Hi all.
Lets assume that we know the following:
[tex]
\sum\limits_{n = - \infty }^\infty {\varepsilon _n (t)} \exp ( - i\omega _n t) = a_0 + \sum\limits_{n = 1}^\infty {\varepsilon _n (t)} \exp ( - i\omega _n t),
[/tex]
where a0 is the contribution for n=0. Now I have an expression for a function f given by the following:
[tex]
f = \sum\limits_{n = - \infty }^\infty {\varepsilon _n (t)} \exp ( - i\omega _n t)\frac{1}{{Z(\omega _n )}}.
[/tex]
Am I allowed to write f as this?:
[tex]
f = a_0 \frac{1}{{Z(\omega _0 )}} + \sum\limits_{n = 1}^\infty {\varepsilon _n (t)} \exp ( - i\omega _n t)\frac{1}{{Z(\omega _n )}},
[/tex]
i.e. substitute the sum? Personally, I think yes, but I am a little unsure, which is why I thought it would be best to check here. Thanks in advance.Niles.