Posts: 684
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Joined: Oct 2008
03/04/2021, 05:23 PM
(This post was last modified: 03/04/2021, 05:30 PM by sheldonison.)
(03/02/2021, 04:56 PM)MphLee Wrote: I suggest you to create a new cross-referenced post with the new date in the title.
Thanks MphLee,
I updated my first post in this thread with the new March 6th invite! See you all there!
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
- Sheldon
Posts: 1,906
Threads: 409
Joined: Feb 2009
was it recorded now ?
Regards
tommy1729
Posts: 900
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Joined: Aug 2007
03/07/2021, 10:42 AM
(This post was last modified: 03/07/2021, 11:08 AM by Gottfried.)
I'll add two links from my work which might be specifically helpful.
One essay on Andy's slog, matrix and matrix-inverse taken by LR-decomposition makes better informed decision possible, how the coefficients of the solution-power series converge when matrixsize is increased
https://math.eretrandre.org/tetrationfor...hp?tid=251
One essay on the slog as comparision with the concept of indefinite summation, where I find an example, where the indefinite summation works to give a valid powerseries, and is shown that the matrix-method is closely related (if not identical!) to the Andy's /Walkers matrixmethod
https://math.eretrandre.org/tetrationfor...hp?tid=709
Two more links:
https://math.eretrandre.org/tetrationfor...74#pid4874
problem of reproducing the identy by (Bb-I)*SLOG =?= I0 this might indicate a principal problem of accuracy of matrix-method, even when dimension is increased/powerseries solution is prolonged
https://math.eretrandre.org/tetrationfor...hp?tid=179 "Exact entries" for the matrix-method by Andrew 13.3.2009. I discussed his found formula, but could not fix the relation with the "regular" method via Schröder function. Moreover, maybe the introduction of the integrals is in fact a *modification* of the Walker/Robbins-method, and not only an explication.
At the moment I feel unable to come over with a quick-shot to put this together; maybe I'll find time and concentration next days. For an introduction into that matrix-thinking I could offer a live-session using zoom where I show my matrix-analyses in action, so anyone who is interested should be able to analyze the above linked articles/essays/postings.
Gottfried
Gottfried Helms, Kassel
Posts: 1,214
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Joined: Dec 2010
Hey, Gottfried I wrote a brief response on your discussion about the indefinite sum. Getting indefinite sums of exponentially bounded functions is surprisingly elementary now, due to Ramanujan (I added some tweaks to his method largely using fractional calculus in my second year of undergrad). So getting \( \sum_{j=1}^s \log^a(j) \) is not very hard, and there exists many formulas for it.
