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Results tagged with riemann-zeta-function
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user 500629
The Riemann zeta function is the function of one complex variable $s$ defined by the series $\zeta(s) = \sum_{n \geq 1} \frac{1}{n^s}$ when $\operatorname{Re}(s)>1$. It admits a meromorphic continuation to $\mathbb{C}$ with only a simple pole at $1$. This function satisfies a functional equation relating the values at $s$ and $1-s$. This is the most simple example of an $L$-function and a central object of number theory.
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Integral with polylogarithm related to Riemann zeta function
I want to ask, whether there is possibility to give closed-form value to such expression;
$$ \int_{0}^1i(1-u)^{-1} u^{s-1} \left[e^{\left(2 \pi u+\frac{\pi s}{2}\right)}Li_{1-s}\left(e^{2\pi i n u} …
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