Observations on power series involving logarithmic singularities

[andydude]

I think you got it. The chopping-of-the-first-row and the diagonal-factorial-matrix parts sounded right. But I think we would need to be able to differentiate tetration reliably (not just the first derivative at zero for example) in order to be able to use it to find pentation or the pentalog/hyper5log via the Abel functional equation. I'm not saying we can't, but I can't think of any method available that gives exact derivatives of tetration yet, but granted, we do have approximations.

Andrew Robbins