elementary superfunctions

[tommy1729]

Yes exactly those formula I was looking for!
However can you shorten them a bit by gathering terms or introducing constants for repeatedly occuring terms?
If possible it would be very preferable to indicate the fixed point, if the super-function is obtained by regular iteration.
Would anyway be good if you could explain how you obtained the formulas or what the idea behind is.

just like ansus you dont seem to realize mathematica just uses a handful solutions and all others are special cases.

notice for instance that EVERY f(x) in this thread are

1) f(x) = polynomial ( see also "logistic map" and " inverse hypergeo " )

2) f(x) = moebius = (a x + b)/(c x + d)

3) f(x) = a + b x^c

and 2) has a closed form solution so all that one needs to do to find the superfunction of e.g. 1 / a x + b is to fill in some variables in the general formula.


at this point , its just that simple.

regards

tommy1729