Describing the beta method using fractional linear transformations

[JmsNxn]

Bo, you are a legend. I just want you to understand where I'm coming from in my descriptions. If you call me out I take it as a badge of honour

Compliments, finetuned like this, are always a nice ingredient of forums like this. Never forget!

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Gottfried, I imagine you could describe the lackluster Matrix representation I made in this post. I just know that the identification is the same--I think much more classical analyst though (everything is a taylor series; euler manipulation; mixed with hard german "normal summation"). I suck at matrices, so I'm sure I misexplained something to do with the 2x2 matrix interpretation, lol.

Sounds all pretty solid to me. Why don't you going to publish? Proven convergence of methods to calculate crescent iteration is a rare thing.
Though I could imagine your proofs could become a bit wobbly if it is about to sending the period to infinity.
I just remember Kouznetsov's solution is asymptotically periodic, did you consider this already?

Also, bo. Covid happened. I was offered the beginnings of a PHD program at U of T--and then bam! Covid. So I couldn't go downtown toronto, I couldn't really see the university. On top of me living with my elderly parents. So I kind of got shoehorned out of taking the scholarship they offered me. I will probably go back into it, but it's up in the air since covid. Like, they offered me a good ride PHD 2 years ago, does that still carry over?

So I'm kind of in academic limbo right now, lol. But I was offered a PHD program at U of T, I just fumbled a bit, and then Covid happened and there was no way with all that chaos. But I do plan to try to work something out again, lol.

But a bunch of mathematicians and physicists know me at U of T for a bunch of dumb shit I've done. So I have a fairly good reputation lol

For example, I was an accepted undergraduate in a graduate level class on analytic number theory, and I got the highest mark in the class out of even the graduate level students. Things like that.... So I'm not all full of shit, bo

It's also important to note, if we're being honest. I do not have my undergraduate. And I was offered a 3 year plan to get my phd without an undergraduate degree. I mostly don't have my undergraduate because I've had a lot of personal problems in my life; but I've always found love in math. And U of T has been really good to me. And I got in good with professors, and I showed my true colours. And I kind of got special treatment   But the only thing not giving me my undergraduate degree is the credit requirements--I have graduate level credits in math; but I don't have all the year 1 year 2 credits you need. (So for example I have a bunch of 4th year calculus credits, but I don't have the initial year 1 calculus credit so it fucks everything up with the degree they hand out, lmao)

What ever, thought I'd be honest to you bo. I'm looking to go back, and hopefully I can try and get the same arrangement, 3 year PHD kind of thing. I'm only 30 years old, I figure I'm still young. I'm sure many people get their PhD at 34. My brother is nearly 40 still working on his phd thesis in korean history, lol. He's gotta write that shit in korean too! God I don't envy him, lol.

But long story short, that's why I don't care about hard publishing my work. No one gives a shit til you have a PHD. I've been offered publishing in low level journals but I always turn it down. Go big or go home. I primarily publish my work on arxiv, and that has served me well. If or when I get my PHD then I'll think about proper journals--like your work. Or any strong work. I'm mostly publishing notices and descriptions of what's going on.

ALSO You said Kouznetsov asymptotically periodic.

There is a proof somewhere that \(b = \eta\) has not quite an almost periodic, so it's not almost periodic, but you can do something to put it in the almost periodic space. Is this what you're talking about Kouznetsozv asymptotically periodic?

Sorry when I hear that I go straight to Hilbert spaces--that was also much more what I was known for at U of T. Hilbert spaces and analytic number theory stuff. lol.