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Posted 2018-12-04, 01:31 AM in reply to Chruser's post "Maclaurin series similar to those of e^x"
has some interesting ones.







For where k is odd an arctan term shows up, sometimes added to a polynomial and/or logarithmic terms. For even k I see only polynomial and logarithmic terms. k = 7 has a much neater form than the others that I've looked at





There may be some other stuff that exists.

Curious that the "base" series is that for the natural log, but an arctan shows up when modifying that series. I remember seeing another relation between ln and arctan as well:

(for x>0...switch the sign on the pi/2 for negative x.)

Last edited by Demosthenes; 2018-12-04 at 01:35 AM.
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