0
$\begingroup$

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.

$\endgroup$
4
  • $\begingroup$ FindSequenceFunction is pretty powerful for this sort of pattern search. $\endgroup$
    – Roman
    Commented Mar 30, 2019 at 9:35
  • $\begingroup$ There is no need to guess. You can always construct the Lagrangian inversion of a series. $\endgroup$ Commented Mar 30, 2019 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. $\endgroup$ Commented Mar 30, 2019 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]} $\endgroup$ Commented Mar 30, 2019 at 11:44

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.