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Analytic series

Calculus (Integrals, Series)
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Riemann
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Analytic series

#1

Post by Riemann » Thu Mar 28, 2019 12:56 pm

Evaluate in a closed form the series:

$$\mathcal{S} = \sum_{n=-\infty}^{\infty} \frac{16}{\left ( 4n^2+n+5 \right )^2}$$
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$
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