By properties, I mean linearity, shifting, commutativity, etc.

I was hoping to evaluate something like

$S_\eta = \dfrac{1}{\beta}\displaystyle\sum_{i\omega} g(i\omega)$

where $g(i\omega) = \dfrac{i\omega-\xi_1}{((i\omega-\xi_2)^2-\xi_3^2)((i\omega-\xi_4)^2-\xi_5^2)}$

by using the results in [this table][1]. If not, would it be best to use partial fraction decomposition or is there another method?


  [1]: https://en.wikipedia.org/wiki/Matsubara_frequency