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 Post subject: An infinite sum
PostPosted: Sat Mar 11, 2017 8:40 pm 

Joined: Sat Nov 14, 2015 6:32 am
Posts: 92
Let $r \in \mathbb{Z}$. Prove that

$$\sum_{n=-\infty}^{\infty} \arctan \left( \frac{\sinh r}{\cosh n} \right) = \pi r $$

(H. Ohtsuka)

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$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$


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