An old paper I did, I think deserves its own thread JmsNxn Ultimate Fellow Posts: 1,176 Threads: 123 Joined: Dec 2010 11/26/2022, 09:23 AM 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   https://arxiv.org/abs/1910.05111 MphLee Long Time Fellow Posts: 373 Threads: 29 Joined: May 2013 12/28/2022, 12:59 PM 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. MSE MphLee Mother Law $$(\sigma+1)0=\sigma (\sigma+1)$$ S Law $$\bigcirc_f^{\lambda}\square_f^{\lambda^+}(g)=\square_g^{\lambda}\bigcirc_g^{\lambda^+}(f)$$ JmsNxn Ultimate Fellow Posts: 1,176 Threads: 123 Joined: Dec 2010 12/30/2022, 02:32 AM (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. 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 Daniel Fellow Posts: 248 Threads: 80 Joined: Aug 2007 12/30/2022, 05:32 AM (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. 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 Better than the term in my first paper - transexponential function. Daniel tommy1729 Ultimate Fellow Posts: 1,859 Threads: 402 Joined: Feb 2009 12/30/2022, 11:39 PM (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   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 « Next Oldest | Next Newest »

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