I am looking for some information about series of the following form $$\sum_{n=0}^\infty x^{P(n)},$$ where $P(n)\in\mathbb{Z}[n]$ and $x\in(0,1)$. I am interested also in their partial sums, i.e. $\sum_{n=a}^b x^{P(n)}$. I know that in general it is impossible to calculate it explicitly. I am looking for some list of such series, their asymptotics, estimations,approximations, theorems about convergence etc. Unfortunately, I didn't find any good source of such data. Where I can find some information ? Are some specific names of such a series which I can use to easily find them ?
2026-04-02 17:42:12.1775151732
Generalized geometrical series and sums
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