using sinh(x) ?

[tommy1729]

How is the fixed point removed? Starting with your equation for TommySexp, only interested in the "z" component, then let x=0,
\( \operatorname{TommySexp_e}(z)= \lim_{n \to \infty } \ln^{[n]} (\operatorname{2sinh}^{[z]}(\exp^{[n]}(0))) \)

This function gives the exact same results for all values of n as the following equivalent equation:
\( \operatorname{TommySexp_e}(z)= \lim_{n \to \infty } \ln^{[n]} (\operatorname{2sinh}^{[z+\operatorname{SuperFunction^{-1}(\exp^{[n]}(0))]}} ) \)

Let \( k=\operatorname{SuperFunction^{-1}(\exp^{[n]}(0))-n \), then the following equation is also exactly equivalent:
\( \operatorname{TommySexp_e}(z)= \lim_{n \to \infty } \ln^{[n]} (\operatorname{SuperFunction(z+k+n)) \) As n goes to infinity, k converges quickly to the approximate value, k=0.067838366 (for n=0: k=-0.0734181, for n=1: k=0.0663658, for n>=2: k=0.067838366)

it is clear that iterations of exp and 2sinh are not exactly equal and thus n and z are not interchangeable ...

regards

tommy1729