On May 8, 2019, at 12:00 PM, Mike Stay <metaweta@gmail.com> wrote: My question is whether given a suitably nice but otherwise arbitrary function of s and think of it as a Dirichlet generating function, can I decompose it into a collection of ordinary generating functions?
An OGF seems to imply a smooth function over a finite region of agreement, where there is some hope to make all precision by including more and more terms. If the function has poles, perhaps you could assume it differentiably finite, and build the poles into the defining DE. But this is just the usual local analysis. I can’t tell what you are hoping for on a global scale? Before asking a question in such broad generality, can you give one or even a few minimal working example(s) showing us what you are aiming for? If you only want equivalence on one point, the question is much easier, and increasingly well studied. A few days ago I gave a nice example for Pi^2 on a thread about unusual integrals. —Brad