08/15/2022, 07:54 AM
(08/15/2022, 06:29 AM)Catullus Wrote: I have an idea for how to define a continuous hyper bouncing factorial!
To do it, you would do polynomial interpolation of, and then do
of that.
I know a lot of people are going to treat your comment as incorrect. But I imagine something like:
\[
\text{slog}(x \Lambda^+) = x + g(x) + o(g(x))\\
\]
As \(x \to \infty\); this is probably possible. This of course relates to what Leo was talking about. And how he described first order difference equations and their relation to abel solutions.
Either way; we are reducing the problem into a linear problem, where \(g\) grows at worse exponentially. Then, yeah. I think Leo is right, that we can construct the Hyper bouncing factorial. In so far as, we need to remember at best this is an existence proof. It is not a constructive proof, just existential. Which Leo is to credit for a lot of this.
