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.

edit: yes now I remember he showed in a different article that \( e^z-1 \) has an entire superfunction, while in the mentioned article he describes the two Abel functions (i.e. inverse superfunctions). Thatswhy I mentioned these articles in reply to your reboarding, that you would make sure that your method is not just that of Walker.

Hmm, I've only read the one paper, and that was before this forum started. I see you referenced a couple others in another thread. You also mentioned having all three as PDF's. Would you be able to email those me, by chance?