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Is there a formula for calculating this series:

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

Thanks!

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2 Answers

up vote 1 down vote accepted

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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