# Any formula for this series $\sum_{i=0}^n x^{i^2}$?

Is there a formula for calculating this series:

$$\sum_{i=0}^n x^{i^2}$$

Thanks!

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Extending Gerry's answer a little, you'll get $$\sum_{i=0}^\infty x^{i^2}=\frac{1}{2}(\vartheta_3(0,x)+1)$$ See here (Eqn. 3) for more.

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No. It's a partial sum of a theta series, q.v.

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