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.
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.