Radius of convergence of complex power series $\sum_{k\geq0} z^{k!}$

Asked Sep 27 '22 at 15:06

Active Sep 27 '22 at 15:06

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I'm struggling a bit with determining convergence radius for complex power series.

Determine radius of convergence for: $\sum_{k\geq0} z^{k!}$.

In previous in exercises I've done $lim_k\rightarrow \infty$ $\rvert ak \rvert^\frac{1}{k}$, but it look to me that $ak$ does not exist, which makes me wonder how to solve this.

Can anyone give me a hint on how to solve this?

Thanks!

asked Sep 27 '22 at 15:06

uoiu

Also: https://math.stackexchange.com/q/595501/42969, https://math.stackexchange.com/q/2813968/42969 – all found with Approach0 – Martin R Sep 27 '22 at 15:09
A bit obvious that the series converges for $z\in [0,1)$ and diverges at $z=1$ – reuns Sep 27 '22 at 19:32

Radius of convergence of complex power series $\sum_{k\geq0} z^{k!}$

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