I came across an article here https://math.eretrandre.org/tetrationfor...p?aid=1187 which has some information about tetration, but it doesn't appear to be published through an official journal or arXiv. There's this result in the MSC database, but there is no document accessible anywhere, so it can't be verified. https://mathscinet.ams.org/msc/msc.html?...earch&ls=s

If you look around on page 15, it almost looks like it is providing an analytic continuation of tetration for any height of tetration (although for very limited bases), even complex numbers or non-integer numbers. Is that actually correct? Do we finally have a way to use tetration for any height?

Even if it is correct though, if it can't be attributed with a reputable source (which neither wikipedia nor a random forum on the internet is), then it can't be cited for anything, so hopefully there's some way to find it through some official outlet.

If you look around on page 15, it almost looks like it is providing an analytic continuation of tetration for any height of tetration (although for very limited bases), even complex numbers or non-integer numbers. Is that actually correct? Do we finally have a way to use tetration for any height?

Even if it is correct though, if it can't be attributed with a reputable source (which neither wikipedia nor a random forum on the internet is), then it can't be cited for anything, so hopefully there's some way to find it through some official outlet.