01/31/2021, 11:52 PM
(This post was last modified: 03/04/2021, 05:25 PM by sheldonison.)

Next Saturday Mar 6th, 1pm eastern, 1800 GMT, invitation to our second monthly Tetration zoom meeting. We will discuss Peter Walker's 1991 paper, http://eretrandre.org/rb/files/Walker1991_111.pdf

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.

First meeting invitation (saved)

Next Saturday Feb 6th, 1pm eastern, 1800 GMT,James Nixon will be presenting the paper he has been working on. My plan it to make this a monthly meeting, first Saturday of each month, so we'll also topics for the 2nd meeting in March. We could discuss Peter Walker's 1991 paper for our 2nd meeting. I look forward to meeting as many of you who are able to attend online!!!

https://us02web.zoom.us/j/89038247428?pwd=UFo1dmVGT21YTHpSbTNqUjMyazUzQT09

Meeting ID: 890 3824 7428

Passcode: 322183

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.

Quote: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.

- The conjecture that Walker's method is an infinitely differentiable but nowhere analytic function defined only at the real axis.

There are many other similar tetration functions, conjectured to be infinitely differentiable but nowhere analytic, such as the "base change" function.

- Does Walker's matrix method converge? How do the individual solutions behave?

- How does Jay's accelerated matrix slog technique work, and does the convergence problem remain?

First meeting invitation (saved)

Next Saturday Feb 6th, 1pm eastern, 1800 GMT,James Nixon will be presenting the paper he has been working on. My plan it to make this a monthly meeting, first Saturday of each month, so we'll also topics for the 2nd meeting in March. We could discuss Peter Walker's 1991 paper for our 2nd meeting. I look forward to meeting as many of you who are able to attend online!!!

https://us02web.zoom.us/j/89038247428?pwd=UFo1dmVGT21YTHpSbTNqUjMyazUzQT09

Meeting ID: 890 3824 7428

Passcode: 322183

- Sheldon