I want to find a complex series convergent on (and only on) the set $$\left\{(z_1,z_2)\in\mathbb{C}^2\vert|z_1||z_2|^e<1\right\}.$$ I assume I should find a sequence $(\mu_n,\nu_n)$ such that $$\limsup_{n\to\infty}\sqrt[\mu_n+\nu_n]{r_1^{\mu_n}r_2^{\nu_n}}=1$$ but I don't know how to find such a sequence.
2026-03-25 11:09:53.1774436993
Multivariate complex series convergent on a given set
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