(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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 a_{0}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.

Best regards,

Niles.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Sums: Substituting two sums

**Physics Forums | Science Articles, Homework Help, Discussion**