using sinh(x) ?

[tommy1729]

thanks for your reply sheldon.

in fact my method is intended for the real line.

for the complex plane it will not work * in its limit form *.

i fact , i wont converge for most nonreal numbers * in its limit form *.

( fixpoints L and L* will work )

to sketch some of the reasons , apart from yours ,

exp exp exp ... exp(z) does not converge for the neighbourhood of any nonreal z.

the identity like functions that commutes with * the limit form * is

id(x) = log log ... id( exp exp ... )

however

x = log log exp exp (x)

but this does not hold for complex z

z =/= log log exp exp (z)

which has ofcourse great consequences ( again for the limit form ! )

i dont have much time , but i think i made some ideas clear.

although slightly on different paths , i think our ideas will merge.

i think i can show that my limit form can be transformed to work for all of z.

later when i have more time.

i had some intuition about those singularities , so it doesnt surprise me.

on the other hand , we might be able to learn more about them , and i thank sheldon for the post and pics.

regards

tommy1729

ps : im still thinking about the base change too , despite not personally appealing to me and ( imho ? ) missing important properties ...[/font]