Funny pictures of sexps

[jaydfox]

I think in Henrici "Applied and computational complex analysis" there are error bounds for the continuation. If I remember right the more iterative steps you do for the continuation the more the size of the original development must increase. But then you can get the transposed coefficients inside arbitrary error bounds.

When I performed analytic extension of the power series, extending to slog(z+1)=0, I had to truncate it. The new power series had a radius still limited by the primary singularities. I didn't take it beyond that point, but based on what I learned from the experience, continuing to extend it like this would have been limited only by the primary singularities, because there are no other singularities in the right-half of the complex plane (for real part greater than 0.31813...), at least not in this particular branch.

Had I continued analytically around one of the primary singularities, then I would have encountered more singularities. I've drawn lots of graphs of the singularities going in the logarithmic direction (clockwise around the upper primary fixed point), but I don't think I have drawn any for going the other direction (where there is a singularity at the origin, for instance).