Thread Rating:
  • 1 Vote(s) - 4 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Ueda - Extension of tetration to real and complex heights
#1
Hi, sometimes I check Google Scholar and Arxiv in order to be updated for new papers in our field and it seems that this extension from Takeji Ueda totally avoided my radar.

https://arxiv.org/pdf/2105.00247.pdf

To be honest  I didn't have time to give it more than a quick look. It actually reminds me a lot of that approach with q-analogs worked out by Vladimir Reshetnikov in 2017. I remember Daniel and James being somehow active on those MO questions so they know better than me for sure. I didn't see any reference to those MO conversations, only to the older Hooshmand, Kouznetzov and Paulsen-Cowjill.  So I can't conclude if original results are presented or the author just grabbed ideas in the air and polished the details and completed the proofs. I post here the link for future references.

MSE MphLee
Mother Law \((\sigma+1)0=\sigma (\sigma+1)\)
S Law \(\bigcirc_f^{\lambda}\square_f^{\lambda^+}(g)=\square_g^{\lambda}\bigcirc_g^{\lambda^+}(f)\)
Reply
#2
(12/01/2021, 09:02 PM)MphLee Wrote: Hi, sometimes I check Google Scholar and Arxiv in order to be updated for new papers in our field and it seems that this extension from Takeji Ueda totally avoided my radar.

https://arxiv.org/pdf/2105.00247.pdf

To be honest  I didn't have time to give it more than a quick look. It actually reminds me a lot of that approach with q-analogs worked out by Vladimir Reshetnikov in 2017. I remember Daniel and James being somehow active on those MO questions so they know better than me for sure. I didn't see any reference to those MO conversations, only to the older Hooshmand, Kouznetzov and Paulsen-Cowjill.  So I can't conclude if original results are presented or the author just grabbed ideas in the air and polished the details and completed the proofs. I post here the link for future references.

Thanks MphLee. This appears to be an original and well thought out work. While not the same as my work, it does seem related in a number of points; combinatorics in Sterling Eq of the second kind and q series for example. I plan on giving the paper a more serious look. Particularly the part on convergences base on the fractal structure.
Daniel
Reply
#3
Hey, Mphlee

This is different than Reshetnikov's work vastly. It's just Hooshmand's construction, but with more finesse. This is a piece wise analytic solution. So it isn't analytic for \(\Re z \in \mathbb{N}\); so sadly, this is something that can be constructed pretty easily.
Reply
#4
Just for as an hobby I tried to plot it and it sucks already at the first derivative.

[Image: image.png]

MSE MphLee
Mother Law \((\sigma+1)0=\sigma (\sigma+1)\)
S Law \(\bigcirc_f^{\lambda}\square_f^{\lambda^+}(g)=\square_g^{\lambda}\bigcirc_g^{\lambda^+}(f)\)
Reply
#5
(05/08/2022, 10:59 PM)MphLee Wrote: Just for as an hobby I tried to plot it and it sucks already at the first derivative.

[Image: image.png]

Lmao!!! Told you!
Reply


Possibly Related Threads…
Thread Author Replies Views Last Post
  Qs on extension of continuous iterations from analytic functs to non-analytic Leo.W 18 1,217 09/18/2022, 09:37 PM
Last Post: tommy1729
  Real Multivalued/Parametrized Iteration Groups bo198214 11 494 09/10/2022, 11:56 AM
Last Post: tommy1729
  Constructive real tetration Daniel 1 129 09/01/2022, 05:41 AM
Last Post: JmsNxn
  On extension to "other" iteration roots Leo.W 34 3,513 08/30/2022, 03:29 AM
Last Post: JmsNxn
  What are the types of complex iteration and tetration? Daniel 5 276 08/17/2022, 02:40 AM
Last Post: JmsNxn
  Real and complex tetration Daniel 1 169 08/17/2022, 01:56 AM
Last Post: JmsNxn
  Complex to real tetration Daniel 1 114 08/14/2022, 04:18 AM
Last Post: JmsNxn
  Constructing a real valued Fibonacci iteration--its relation to \(1/1+z\) JmsNxn 7 272 08/13/2022, 12:05 AM
Last Post: JmsNxn
Question Convergent Complex Tetration Bases With the Most and Least Imaginary Parts Catullus 0 151 07/10/2022, 06:22 AM
Last Post: Catullus
  Tetration extension for bases between 1 and eta dantheman163 23 35,914 07/05/2022, 04:10 PM
Last Post: Leo.W



Users browsing this thread: 1 Guest(s)