Convergence Domain $\{|z|+|w| < 1\}$

Question

Construct a power series whose domain of convergence is $\{(z, w) \in \mathbb{C}^2 : |z|+|w| < 1\}$

Having a bit of trouble with this problem, and was wondering if anyone had any ideas. There's a similar problem here: Convergence domain: $\{(z,w):|z|^2+|w|^2 < 1\}$, but this domain is a bit trickier.

Any help would be appreciated. Thanks

Answer 1

$\sum_{k=0}^\infty (z + e^{ik} w)^k$ from the answer in the question you linked (just with the squares removed) should work, for the same reason.