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I understand that $$\prod\limits_{m=1}^N \left(1-R^mA\right)$$ is a polynomial in $A$, and so can be written as $\sum\limits_{k=0}^N c_k A^k$ for some coefficients $c_k$.

I can't seem to figure out a closed form expression of $c_k$, any ideas?

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  • $\begingroup$ See the $q$-Pochhammer symbol. $\endgroup$ – orlp Oct 2 '17 at 15:30
  • $\begingroup$ What do you actually need? A closed-form formula, just a formula or an algorithm? $\endgroup$ – Lwins Oct 2 '17 at 15:44
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Is the formula (4) on http://mathworld.wolfram.com/q-PochhammerSymbol.html what you want?

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  • $\begingroup$ @Tiana The site has references for those symbols. You can have a check if you are not familiar with them. $\endgroup$ – Lwins Oct 2 '17 at 16:09
  • $\begingroup$ would $c_k$ then be be $(-1)^k$ multiplied with everything else apart from $a^k$? thanks $\endgroup$ – Tiana Oct 2 '17 at 16:12
  • $\begingroup$ @Tiana Sure, you got it. $\endgroup$ – Lwins Oct 2 '17 at 16:13

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