Prove the series <munderover> &#x2211;<!-- ∑ --> <mrow class="MJX-TeXAtom-ORD"> n

Arraryeldergox2

Arraryeldergox2

Answered question

2022-06-22

Prove the series
n = 1 2 z z 2 n 2

Answer & Explanation

luisjoseblash2

luisjoseblash2

Beginner2022-06-23Added 16 answers

Fix k. For | z k | < 1 2 the series n k | 2 z z 2 n 2 | is dominated by n k 2 | k | + 1 n 2 ( | k | + 1 2 ) 2 and hence this sum is analytic in | z k | < 1 2

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