I already compute the Laurent series, which is pretty easy using the Taylor series of both. Then I Know that we can define a branch cut for the square root function in $[1,\infty)$. And we can say that the $e^{\frac{1}{z}}$ converges for $|z| > 0$. Then I have that in that branch cut the radius of convergence is $R = 1$ and I can say that it converges uniformly in $Ann(0,0,1)$. However, they ask me to discuss convergence at $|z| =1$ and I'm having problems with that. This series I know that at $(1,0)$ it can not converge since it's in the branch, but in the rest of the circle? and what can I say for $|z| > 1$?
2026-04-02 07:06:11.1775113571
What is domain of convergence for the Laurent series of $\sqrt{1-z} + e^\frac{1}{z}$?
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