I am trying to understand how to calculate the domain of convergence for the series [From: Tasty Bits of Several Complex Variables] :
$$ \sum_{j,k} c_{j,k}\; z_1^j z_2^k $$
But I don't really understand how to handle the $c_{j,k}$ term. I saw a past post(and a few more but they did not help me either), but I don't understand the result it presents. (Of course the other examples like $\sum_{k}z_1 z_2^k$, $\sum_{j,k} z_1^j z_2^k$, are very clear.)
Can we actually derive some general result for any $c_{j,k}$? Or do we need some information about it?
The domain of convergence is a logarithmically convex complete Reinhardt domain, and nothing more can be said without knowing what the coefficients are. Every such domain is the domain of convergence for some power series.