Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Is there a formula for calculating this series:

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


share|cite|improve this question

2 Answers 2

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.

share|cite|improve this answer

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

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.