What is the radius of convergence of a power series in two real variables?
If I were to fix one of the variables (i.e. make it a real constant), then would the radius of convergence simply be related to the nearest singularity?
2026-03-27 11:48:07.1774612087
What is the radius of convergence of a power series in two variables?
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A power series in several complex variables doesn't have a radius of convergence. In general, the domain of convergence is a logaritmically convex Reinhardt domain, but not necessarily a ball. Consider for example the series $$\sum_{k=0}^\infty z^k w^k \qquad\text{and}\qquad \sum_{j=0}^\infty \sum_{k=0}^\infty z^j w^k$$ respectively.