temporary fruit

\sum_{n=0}^{\infty} \frac{1}{e^{7n^{2}+70n+173}} = e^{2}\left[\frac{\theta_{3}(0,1/e^{7})+1}{2} - \sum_{n=0}^{4} (1/e^{7})^{n^2}\right]

According to Wolfram Alpha, the left side is:


and the right side is


This is a fruit of my attempt to find a general formula for

\sum_{n=0}^{\infty} q^{an^{2}+bn+c}, |q|<1.


One response to “temporary fruit

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