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Is there a formula for calculating this series:

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

Thanks!

2 Answers 2

1

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.

4

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