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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. If not, would it be best to use partial fraction decomposition or is there another method?

By properties such as linearity, shifting, commutativity, etc. I was hoping to evaluate something like,

$$S_\eta = \dfrac{1}{\beta}\displaystyle\sum_{i\omega} \dfrac{i\omega-\xi_1}{[(i\omega-\xi_2)^2-\xi_3^2][(i\omega-\xi_4)^2-\xi_5^2]}$$

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

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. If not, would it be best to use partial fraction decomposition or is there another method?

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. If not, would it be best to use partial fraction decomposition or is there another method?

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. If not, would it be best to use partial fraction decomposition or is there another method?

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. If not, would it be best to use partial fraction decomposition or is there another method?