Funny pictures of sexps

[jaydfox]

Indeed there is no singularity visible inside the circle with radius 1.5.
But one can see that to the right side the lines become dense which may count numerically as a singularity and thatswhy does not allow the sexp at 0 to converge for r>1.4.

Count "numerically" as a singularity? It's not a singularity, so at best it means that you just need more terms in the power series. And as mentioned before, you must truncate the slog series before reverting, or of course you'll get bizarre results. But the closest singularity is at -2, so that is what limits the radius of convergence.

When I reverted a 600-term truncation of a 1200-term slog, I got a sexp function that approximated the logarithmic singularity at x=-2 very nicely. Indeed, I was able to "remove" the singularity by subtracting the taylor series for log(x+2), and confirm that the residue had an approximately double logarithmic singularity at x=-3. In fact, the Taylor series for sexp will converge on the Taylor series for log(log(x+3)), as this accurately depicts the two closest singularities (well, three technically: one at -2, and one each at -3 in the clockwise and counterclockwise windings to the left of the first). I'm pretty sure I've described this at some point in the past, which is to say that I vaguely recall discussing it with you or Andrew, and I can't imagine that we discussed it anywhere but in the forum; I'll see if I can find it.