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One more thing just to perhaps head off future problems: I found this because I was trying to autodiff some code, so eventually I want to get derivatives.
I wonder if we could add a unit test for the derivatives computed via ForwardDiff? To wit, maybe use $z \frac{\partial Li_s}{\partial_z} = Li_{s-1}(z)$?
Good point, but there are such unit test already. :)
To be precise, there are tests for the real functions li0, reli1, reli2, reli3, reli4 and the general reli. To find the tests, just grep ForwardDiff test/*.jl. They have been implemented by @longemen3000 when he added the support for ForwardDiff and ChainRules.
Back then, @longemen3000 said that ForwardDiff does support derivatives of (holomorphic) complex functions. When this is added, the complex polylogarithms will get derivative support as well (including tests).
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See issue #40