1
$\begingroup$

I'm trying to find a way to evaluate this sum (found by Haldane in Phys. Rev. Lett. 60, 635 (1988): $$S_{pq}=\sum_{n=1}^{N-1} z^{nJ} (1-z^{n})^{p-1}(1-z^{-n})^{q-1}$$ with $z= e^{\frac{2i\pi}{N}}$ and $0\leq J\leq N$ if someone have an idea, let me know, Thanks

$\endgroup$
0
$\begingroup$

Hint: You can use the binomial expansion and then simplify back with the N-th roots of the unit $\exp{(\frac{2i\pi}{N})}$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.