I hope you all can forgive my naivety but I found this on MathSE. It somehow seems familiar but at the same time, since I missed a lot of the nitty gritty details of the tetration extensions in the past discussions (not the beta method ones), it somehow look new to me.

In this question How to evaluate fractional tetrations? (March 2020) the user Simply Beautiful Art cites a chain of previous question of his/her, and in that the author claim the method is probably equivalent to Kneser. The formula is derived from the assumption of asymptotic behavior analogous to that of Gamma function.

The chain of questions where this is laid out are:

Dec 26, 2019 Numerical instability of an extended tetration

Dec 26, 2019 Verifying tetration properties

Dec 29, 2019 Verifying uniqueness of my tetration

Of the three only the first received attention by forum users (Gottfried). There only the question if computation was unstable of the formula non-convergent was treated. The other posts maybe were not noticed by the forum experts. So my question: is it something new? Was already discussed here?

In this question How to evaluate fractional tetrations? (March 2020) the user Simply Beautiful Art cites a chain of previous question of his/her, and in that the author claim the method is probably equivalent to Kneser. The formula is derived from the assumption of asymptotic behavior analogous to that of Gamma function.

The chain of questions where this is laid out are:

Dec 26, 2019 Numerical instability of an extended tetration

Dec 26, 2019 Verifying tetration properties

Dec 29, 2019 Verifying uniqueness of my tetration

Of the three only the first received attention by forum users (Gottfried). There only the question if computation was unstable of the formula non-convergent was treated. The other posts maybe were not noticed by the forum experts. So my question: is it something new? Was already discussed here?