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Closed forms of Nielsen polylogarithms $\int_0^1\frac{(\ln t)^{n-1}(\ln(1-z\,t))^p}{t}dt$?
(This summarizes my posts on Nielsen polylogs.)
I. Question 1: How to complete the table below? Consider the special cases $z=-1$ and $z=\frac12$. Given the Nielsen generalized polylogarithm,
$$S_{n,...
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15
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Known exact values of the $\operatorname{Li}_3$ function
We know some exact values of the trilogarithm $\operatorname{Li}_3$ function.
Known real analytic values for $\operatorname{Li}_3$:
$\operatorname{Li}_3(-1)=-\frac{3}{4} \zeta(3)$
$\operatorname{Li}...
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