<s>[INST] A question about meaning of a notation When we have a sum of the form 
$$ \sum_{cyc} \dfrac{ (a+b)(a+c) - bc }{(b-c)(b^3-c^3)} $$
Does this mean: 
$$ \dfrac{ (a+b)(a+c) - bc }{(b-c)(b^3-c^3)} + \dfrac{ (b+c)(b+a) - ac }{(a-c)(a^3-c^3)} + \dfrac{ (c+b)(c+a) - ba }{(b-a)(b^3-a^3)} $$ 
?
 [/INST] It means that you take the sum over the cycles based on  $(a \ b \ c)$ which are 
$$\begin{cases}
(a \ b \ c) \to (a \ b \ c)\\
(a \ b \ c) \to (b \ c \ a)\\
(a \ b \ c) \to (c \ a \ b)
\end{cases}$$
</s>