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Many special functions appear as solutions of differential equations or integrals of elementary functions. Most special functions have relationships with representation theory of Lie groups.

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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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