Funny pictures of sexps

[jaydfox]

Well I am not completely sure what you mean with recentering. But is that still applicable with my previous explanations?

It doesn't seem so, yet this behavior is so strikingly familiar to problems I experienced that somehow it must be similar. See my next comments.

Anyway here are the root tests (however only until 100, because creating the Carleman matrix at non-0 is really time consumptive)

If you look at the first two graphs for islog_e at 0 and 1, you should be able to see the effect I was describing. For the series developed at 0, there would seem to be a radius of convergence indicated asymptotically, until at about the 85th term the terms would seem to become inaccurate. For the series developed at 1, we again see a radius indicated asymptotically, but then somewhere around the 60th term, the effect is ruined, much earlier. Out of curiosity, if you recentered it to x=1.5 (outside the original radius of convergence), does the system solve properly?

If you try reverting the 60-term truncation for the series developed at x=1, you will likely see much better behavior of the isexp_e power series. Try it and let me know.

Update: Ach, I was looking at your graphs upside down! I always neglect the negation when using the root test, so I look at the reciprocal of the apparent radius of convergence. So where you graphs shoot up right at the end, mine would have shot down. So perhaps I'm misinterpreting your results.