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Tagged with polylogarithm zeta-functions
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Do all complex zeros of $Li_s(z)\,- \, Li_{1-s}(z)$ get the shape $s=\dfrac12 + \dfrac{k \, \pi }{\,\ln(2)}\,i$ when $z \rightarrow 0^{-}$?
This is a subquestion of this question on MO.
Numerical evidence strongly suggests that when $z \rightarrow 0^{-}$ the complex zeros that lie in the critical strip $0 \lt \Re(s) < 1$ of:
$$Li_s(z)...
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How to solve this summation (Lerch Transcendent)?
How is it possible to deduce the closed form of the following?
$$\sum_{i = 0}^{n - 1} \frac{2^i}{n - i} = ?$$
