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 \(\bigcirc_f^{\lambda}\square_f^{\lambda^+}(g)=\square_g^{\lambda}\bigcirc_g^{\lambda^+}(f)\)
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#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
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#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.
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#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 \(\bigcirc_f^{\lambda}\square_f^{\lambda^+}(g)=\square_g^{\lambda}\bigcirc_g^{\lambda^+}(f)\)
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#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!
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