But you're not addressing the issue that the reason to cite it would be the premise that it interpolates tetration for fractional heights.
The claim in the paper J.N. paper appears to be that any complex height z can be represented with a standard analytic series and integral, there's nothing particularly tricky about that beyond calculus. The question is whether or not it can actually be interpreted as defining tetration for any complex fractional height. This is supposed to be THE home site for tetration, and so far it's been extraordinarily disappointing.
The recent paper states in (15) a definition of fractional iterates of the exponential function. Okay, great, I'd love if there was such a thing. The problem is it defines them in terms of newly defined functions ksexp and kslog which isn't even conventional notation to begin with.
Then, when I look at how the paper defines ksexp and kslog, it refuses to. What's even worse is I see in the paper " Unfortunately it lacks a proof of convergence ". And then even in your post you make up yet another notation "tet_b."
Hopefully, you will catch up and understand that it is the author's burden to effectively communicate their ideas. Even if someone comes up with a proof for the Riemann hypothesis, it's completely useless if no one can interpret it.
The problem has nothing to do with level, it's the problem of consistency and clarity as the fundamental reason that tetration is not widely used. Who do you think would end up using such a formula? Physicists, computer scientists, astronomers, chemists, etc, they don't specialize in pure math because they're busy doing research on physical phenomena and it's the job of mathematicians to explain their tools for them.
The claim in the paper J.N. paper appears to be that any complex height z can be represented with a standard analytic series and integral, there's nothing particularly tricky about that beyond calculus. The question is whether or not it can actually be interpreted as defining tetration for any complex fractional height. This is supposed to be THE home site for tetration, and so far it's been extraordinarily disappointing.
The recent paper states in (15) a definition of fractional iterates of the exponential function. Okay, great, I'd love if there was such a thing. The problem is it defines them in terms of newly defined functions ksexp and kslog which isn't even conventional notation to begin with.
Then, when I look at how the paper defines ksexp and kslog, it refuses to. What's even worse is I see in the paper " Unfortunately it lacks a proof of convergence ". And then even in your post you make up yet another notation "tet_b."
Hopefully, you will catch up and understand that it is the author's burden to effectively communicate their ideas. Even if someone comes up with a proof for the Riemann hypothesis, it's completely useless if no one can interpret it.
The problem has nothing to do with level, it's the problem of consistency and clarity as the fundamental reason that tetration is not widely used. Who do you think would end up using such a formula? Physicists, computer scientists, astronomers, chemists, etc, they don't specialize in pure math because they're busy doing research on physical phenomena and it's the job of mathematicians to explain their tools for them.