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How to compute $$\sum_{j=1}^{K}\frac{P(j)}{Q(j)}\exp(2\pi ija) $$ where $\left|a\right|<1,\ K\in Z$,$\frac{P(j)}{Q(j)}$-rational function.Roots $Q(j)$ are known, complex.$$$$ In my case $$Q(j)=(1+j^{2q})(j^{2p}+(j-A)^{2p})$$ with integer $q,p>0$ and real $A>=0$.

$$P(j)=(j-A)^{2p}$$ or $$P(j)=(j)^{2p}$$ or $$P(j)=(j)^{2}(j-A)^{2p}$$

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Numerically?$\,$ –  J. M. May 2 '11 at 11:28
    
Why $|a|<1$? But $K$ should be positive, presumably? –  Did May 2 '11 at 12:03
    
J.M not numerically,but but some approximation mistake is ok –  Katja May 2 '11 at 12:09
    
Didier Piau, K is positive, integer. $\left|a\right|<1$ in my case. I don't know if it is helpful –  Katja May 2 '11 at 12:12
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@Katja: If $Q(j)$ is so simple, maybe $P(j)$ can also be provided in the question? And yes: what is $x$? –  Fabian May 2 '11 at 19:16

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