# Can I use inbuilt machine learning to guess the n-th term of the inverse series?

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.

• FindSequenceFunction is pretty powerful for this sort of pattern search. – Roman Mar 30 '19 at 9:35
• There is no need to guess. You can always construct the Lagrangian inversion of a series. – J. M.'s technical difficulties Mar 30 '19 at 9:36
• 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. – Quasar Supernova Mar 30 '19 at 11:23
• 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),3/2-2/Sqrt,-3+10 Sqrt[2/3]-15/(2 Sqrt),475/12+45/Sqrt-35 Sqrt-24/Sqrt,-315+252 Sqrt[2/5]-7315/(12 Sqrt)+70 Sqrt+190 Sqrt} – Quasar Supernova Mar 30 '19 at 11:44