Consider this concrete example.

InverseSeries[ Series[ PolyLog[s, z], {z, 0, 10}]]

From this output is there a way of writing down a formula for the n-th term? I mean can I guess all the other terms beyond what is being displayed using machine learning subroutines or whatever.

  • $\begingroup$ FindSequenceFunction is pretty powerful for this sort of pattern search. $\endgroup$ – Roman Mar 30 '19 at 9:35
  • $\begingroup$ There is no need to guess. You can always construct the Lagrangian inversion of a series. $\endgroup$ – J. M.'s technical difficulties Mar 30 '19 at 9:36
  • $\begingroup$ Ok J.M. thanks. I did the Lagrange inversion and got a whole bunch of coefficients called g(n). I can list them one by one for the PolyLog[3/2,z] function but I really need some way of guessing a closed form of the n-th term in terms of some managable function of n. $\endgroup$ – Quasar Supernova Mar 30 '19 at 11:23
  • $\begingroup$ Here are the first 6 g(n)'s for PolyLog[3/2,z] inversion as per wiki notation. Seventh term onwards is taking forever: {1,-(1/Sqrt[2]),3/2-2/Sqrt[3],-3+10 Sqrt[2/3]-15/(2 Sqrt[2]),475/12+45/Sqrt[2]-35 Sqrt[3]-24/Sqrt[5],-315+252 Sqrt[2/5]-7315/(12 Sqrt[2])+70 Sqrt[3]+190 Sqrt[6]} $\endgroup$ – Quasar Supernova Mar 30 '19 at 11:44

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