I don't know how to compute $\sum_{n\in\mathbb{Z}}\exp(-|n|^\frac{1}{2})$. I think this series is convergent because after breaking the sum into three parts, I need to check the convergence of $\sum_{n\geq 1}\exp(-n^\frac{1}{2})$, which is convergent by comparing to $\sum_{n\geq 1}\frac{1}{n^2}$. However I have no idea on how to compute the sum itself. Thanks for any help.
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@geetha290krm Sorry I forgot the absolute value. – xuanphong Jan 20 '23 at 10:03
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2Does it have a closed form? – Sine of the Time Jan 20 '23 at 10:31
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https://math.stackexchange.com/questions/2109313/does-sum-q-sqrt-n-converge – Jotabeta Jan 20 '23 at 10:32
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@SineoftheTime I don´t know if there is a closed form actually. – xuanphong Jan 20 '23 at 11:09