I tried to convert this infinite sum into an defined integral, for easier caluclations. The Problem i don't have much experience with sums or even the Riemann sum. I tried my best to solve it, but i couldn't find a resource that describes hvo you convert a complex function into an integral.
$$\lim_{k \to \infty}\sum_{n = 1}^{k}(-1)^{n-1}\cdot n^{-x}\cdot n^{-iy}$$
My try is this integral, which only works when $x = 1$: $$\int_{1}^{\infty}(-1)^{n-1}*n^{-iy} dn \Leftarrow x = 1$$ But i'm very sure that this is wrong
Any ideas are welcome :)