I'm attempting an integration of such a function. Mathematica won't help me and I've tried several series decompositions which haven't yielded much yet.
So I'm after: $\int_{-\infty}^{\infty}\mathrm{Li}_n^2(-\alpha e^{-\beta x^2})\,\mathrm{d}x$
If the general Polylogarithm can't be done I could suffice with $Li_1$, but not ideal.
Edit: If this is not the appropriate place for such a question let me know and I will remove it, googling of Polylogarithms brought me here (!).