Outline of Proof
After subtracting a constant from, we may assume that . Let . Then substituting and performing a simple manipulation of the series results in
Given, pick n large enough so that for all and note that
when z lies within the given Stoltz angle. Whenever z is sufficiently close to 1 we have
so that when z is both sufficiently close to 1 and within the Stoltz angle.
Read more about this topic: Abel's Theorem
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