Is there some simplifying expression for the sum
$$\sum_{n=1}^\infty \frac{1}{|an+b|^x}$$
where $a,b$ are arbitrary real numbers, and $x$ is a real number larger than 1 (which should ensure convergence)? (This is a more general version of the question Calculating squared reciprocals of arithmetic series , and I have not found it brought up in other threads.) Going one step further, is there an expression for the sum
$$\sum_{n=1}^\infty \frac{n}{|an+b|^y},$$
as well, where $y$ is a real number larger than 2? I see that in principle one could approximate the sums by integrals, but are there any exact expressions in terms of more "well-known" (even if not necessarily elementary) functions?