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I have run across the series $\sum_{n=0}^\infty x^{2^n}$. Does this series have a name or a label? I can't find one, but it seems too simple not to already have a name.

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    The special series does not have a name, but these kind of series with gaps have specific properties and are named after Ostrowski and Hadamard. https://en.wikipedia.org/wiki/Ostrowski%E2%80%93Hadamard_gap_theorem – Torsten Feb 07 '25 at 14:35
  • This question is a duplicate of What is the name of this type of series?, see in particular this answer. If you believe it’s different, please [edit] the question, make it clear how it’s different and/or how the answers on that question are not helpful for your problem. PS. Duplicate has been found with this approach0 search. – Martin Brandenburg Feb 07 '25 at 14:38
  • See also https://math.stackexchange.com/questions/3027545/lacunary-function-doesnt-converge-anywhere-on-the-boundary and https://math.stackexchange.com/questions/2067687/lacunary-series-finding-a-limit and https://math.stackexchange.com/questions/5021695/on-the-uniqueness-of-an-analytic-continuation-for-the-lacunary-series-sum-n-0 – Martin Brandenburg Feb 07 '25 at 14:44

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