An old paper I did, I think deserves its own thread
#1
Hey, everyone. Before there was the \(\beta\)-method, there was the \(\Upsilon\) solution.

This paper is essentially on solving the equation:

$$
y(s+1) - y(s) = e^{sy(s)}\\
$$

And how iteration/recursion can be used to describe a holomorphic solution to this equation. (Think: really fancy continued fractions, but with nested compositions.)

This paper really put me on the map at U of T; especially, with a couple of professors. So I think it deserves its place here. Plus, it's super exponential and looks a lot like tetration (hence, inspiring the \(\beta\)-method).

Hope everyone's doing well Smile 

https://arxiv.org/abs/1910.05111
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#2
I always loved the introduction. It is inspired and sublime as most of your papers. To bad that it is impossible for me to digest the topic once you hit the gas with your wall sof conditions for theorems and lemmas. Tongue

MSE MphLee
Mother Law \((\sigma+1)0=\sigma (\sigma+1)\)
S Law \(\bigcirc_f^{\lambda}\square_f^{\lambda^+}(g)=\square_g^{\lambda}\bigcirc_g^{\lambda^+}(f)\)
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#3
(12/28/2022, 12:59 PM)MphLee Wrote: I always loved the introduction. It is inspired and sublime as most of your papers. To bad that it is impossible for me to digest the topic once you hit the gas with your wall sof conditions for theorems and lemmas. Tongue

My friend who's a philosophy major; and who is a published analytic philosopher, hated my introduction. "Why are you sexualizing the Gamma function...?"

I mean, if you don't think the Gamma function is sexy as fuck, maybe math just ain't for you Big Grin
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#4
(12/30/2022, 02:32 AM)JmsNxn Wrote:
(12/28/2022, 12:59 PM)MphLee Wrote: I always loved the introduction. It is inspired and sublime as most of your papers. To bad that it is impossible for me to digest the topic once you hit the gas with your wall sof conditions for theorems and lemmas. Tongue

My friend who's a philosophy major; and who is a published analytic philosopher, hated my introduction. "Why are you sexualizing the Gamma function...?"

I mean, if you don't think the Gamma function is sexy as fuck, maybe math just ain't for you Big Grin

Better than the term in my first paper - transexponential function. Wink
Daniel
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#5
(11/26/2022, 09:23 AM)JmsNxn Wrote: Hey, everyone. Before there was the \(\beta\)-method, there was the \(\Upsilon\) solution.

This paper is essentially on solving the equation:

$$
y(s+1) - y(s) = e^{sy(s)}\\
$$

And how iteration/recursion can be used to describe a holomorphic solution to this equation. (Think: really fancy continued fractions, but with nested compositions.)

This paper really put me on the map at U of T; especially, with a couple of professors. So I think it deserves its place here. Plus, it's super exponential and looks a lot like tetration (hence, inspiring the \(\beta\)-method).

Hope everyone's doing well Smile 

https://arxiv.org/abs/1910.05111

It is a nice paper.

I have seen it before when i was on arxiv looking for you or tetration.

I need to think about it.

It is nice but im unsure how to continue.

regards

tommy1729
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