Is there a formula for calculating this series:
$$ \sum_{i=0}^n x^{i^2} $$
Thanks!
Is there a formula for calculating this series:
$$ \sum_{i=0}^n x^{i^2} $$
Thanks!
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.
No. It's a partial sum of a theta series, q.v.