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[jaydfox]

I don't mean to be pedantic, but if I recall correctly, when I had investigated this line before, I found that the radius of convergence could be adversely affected when the power series was developed at a point other than 0, and truncation of the computed power series became necessary.

The powerseries should have as convergence radius the distance from the development point to the fixed point. (If we assume that the islog has no other singularities than the primary fixed point(s))

Well, yes, the infinite power series will have such a radius. I'm speaking of what happens when we look at finite truncations.

Perhaps an easier example is to look at the power series for log(x+1). Truncate it to 100 terms and recenter the power series to x=0.25 (which would be equivalent to log(x+1.25). The infinite power series will have a radius of 1.25.

However, out of curiosity, what does the root test indicate the radius would appear to be, if you look at terms 70-90?

Try again with 200 terms, recenter, and look at the radius apparently indicated by the first 80 terms. Now look at the radius indicated by terms 140 to 170. See a pattern?

Recentering a finite truncation of the infinite power series does not readjust the radius of convergence. However, if we truncate the (already truncated) series at a suitable spot, then we can get a correct view. Thus, if we solve a 100 term system at one point, and then recenter, we must truncate to a shorter series, perhaps 25-50 terms, depending on how far we moved the system. If we move it outside the original radius of convergence, we must do so in multiple steps, each remaining within the radius of convergence, and each time we must truncate the series appropriately.

This is a effect of the underlying polynomial truncations, so although your method is different, I would be very surprised if the same effect was not tainting your results. Try using a truncation of only the first half of the terms you calculated, and see if these issues persist.