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**Closed form for "geometricish" series (index squared in the exponent)?**

Hi all,

Is there a nice closed form for the following series?

[itex]\sum_{k=0}^n x^{k^2}[/itex]

Even a decently tight upper bound and lower bound would be nice (obviously it is bounded by the corresponding geometric series [itex]\sum x^k[/itex], but is there anything better?).

Thanks!