The "cheta" function

[jaydfox]

Where is the definition? Until now I only saw formulas that use non-integer iteration.
Then it seems cheta is just a superfunction of \( e^{x/e} \).
The question suggests itself, whether cheta and heta are just the two regular iterations of \( e^{x/e} \), i.e. the ones that Walker describes in his article; as far as I remember they are entire.

Hmm, that sparked a memory of a long-forgotten converstation we had:
http://math.eretrandre.org/tetrationforu...ght=entire

It's amazing how much more sense all of that makes now (and clear from my posts where my misunderstandings at the time were, as well as my gaps in understanding complex analysis). And yes, looking at just the descriptions in that old discussion, it would appear that cheta is nothing new.

The bright side is, this saves me the work of having to rigorously prove various properties, as they apparently have been proven for nearly 20 years. I need only work on getting good numerical approximations (several thousands of bits of accuracy), to use in my change-of-base formula.