Maybe the solution can be useful to somebody:
the expression f(N,z) =\left(\sum_{j'=0}^{N}j'exp(-ij'z)\right)\left(\sum_{k'=0}^{N}j'exp(ik'z)\right) was solved recalling that:
\sum_{l=0}^Nle^{ly} = \sum_{l=0}^N\frac{\partial e^{ly}}{\partial y} =...
Thank you very much, this seems to be the easiest, and also most elegant, solution.
Just the last question, the sum can also go from 0 to N? It should make no difference since for j = 0, j\cdot e^{ijx} = 0
Hello everybody,
I have some problems in finding an analytical expression for this product:
\sum_{j=0}^{N}(N-j)e^{-ijy}\cdot\sum_{k=0}^{N}(N-k)e^{iky} .
I have solved the problem for several Ns, applying the Euler rule 2\cos(x) = e^{ix} + e^{-ix}
Now, I'm trying to express the...