I have the following problem:
[![page1](https://i.stack.imgur.com/H8gzr.jpg)](https://i.stack.imgur.com/H8gzr.jpg)

I am trying to see how to approach part (iii) Abel's theorem.
I took the suggestion of @Halbaroth below. But, I don't get very far.

It looks like a simple substitution will give me $F(z\_1)$, but it seems too straightforward and I did not do any translations or rotations to reduce the case considered in (ii). In (ii) $lim\_{r \to 1−}$ in this case $lim\_{r \to R−}$, how can I apply (ii) directly? I think I am still missing something - and its not a simple substitution. Basically by direct substitution, I have $lim\_{r \to R^-} \sum\_{0}^{\infty} F(z\_0+re^{i \theta})=lim\_{r \to R^-} \sum\_{0}^{\infty} a\_n(z\_0 +re^{i \theta}-z\_0)^n = F(z\_1)=F(z\_0+Re{i \theta}) = \sum\_{0}^{\infty} a\_n(z\_0+Re^{i \theta} - z\_0)^n$.

I don't think this is right.