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I am unable to answer important questions such as what is the inverse of PolyLog[3/2,z]? I mean can you express the solution to w = PolyLog[3/2,z] (solve for z in terms of w) in terms of functions known to Mathematica?

Also what does the large z expansion of PolyLog[3/2,z] and PolyLog[5/2,z] look like?

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  • $\begingroup$ I do not believe there is a closed form for the inverse of a polylogarithm, but it should not be too hard to construct series expressions: InverseSeries[Series[PolyLog[3/2, x], {x, 0, 5}]] // Simplify. As for asymptotics, have you already seen this? $\endgroup$ – J. M. will be back soon Mar 30 at 7:47
  • $\begingroup$ Thanks for this. Yes I knew about the wiki. But my comment was in the context of Mathematica. The asymptotic expansion returns unevaluated rather than giving me the wiki answer. Is this also because I am using an outdated version of Mathematica? $\endgroup$ – Quasar Supernova Mar 30 at 8:47
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    $\begingroup$ No, I don't think Mathematica is smart enough to know the asymptotic expansion of the polylogarithm (see e.g. this older thread). $\endgroup$ – J. M. will be back soon Mar 30 at 8:54
  • $\begingroup$ For the second part of your question, look here: functions.wolfram.com/ZetaFunctionsandPolylogarithms/PolyLog/06/… $\endgroup$ – Roman Mar 30 at 13:54

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