Sat March 6th second Tetration mtg; Peter Walker's 1991 paper

[sheldonison]

Sadly I won't be there because I'm busy... but it is a great idea. I'd be able to understand much faster the key concept listening to a presentation from the author. Too bad.
I hope you will update the forum if some new insight  or progress will be achieved during the zoom call.

Thanks James for a superbly written paper, especially the first half of your paper where you carefully prove the convergence of \( \phi(s) \), and that it is entire. We had a good meeting with Sheldon, James, Henryk Trapmann, Gottfried Helms, and Cheetahs.  James wasn't feeling well so we didn't go through his paper in much detail.  It was good to actually see and talk to Henryk and Gottfried, and of course James.  I'll setup a second zoom meeting Sat Mar 6th, also 1800 GMT; 1pm east coast time.   

https://us02web.zoom.us/j/89038247428?pwd=UFo1dmVGT21YTHpSbTNqUjMyazUzQT09
Meeting ID: 890 3824 7428
Passcode: 322183

I would like to discuss Peter Walker's 1991 paper.  Peter Walker's paper discusses generating the Abel function for iterating \( \exp(x)\mapsto\exp(x)-1 \), and then using it to generate tetration/slog for base e.  The paper also includes what was reinvented by Andrew as the matrix equation slog, which is the most accessible version of tetration/slog I know of.  And Peter Walker asks whether these two functions agree with Kneser's conformal mapping tetration function.  I would like to revisit Peter Walker's paper discussing other developments on this forum since that time, especially discussing the last paragraph with some updated results on these two methods from the past 10 years mostly from this forum.

These differences cannot be explained without at least a proof of convergence
of the matrix method. And we cannot identify our function defined by the
iteration method ... with Kneser's function defined by conformal mappings,
without an extension of the domain of the function h to include nonreal values.
Until both these difficulties have been overcome, the possibility remains that
either two or three distinct generalized logarithms have been constructed.