(07/10/2010, 05:17 AM)bo198214 Wrote: Another formula (2.29 in the overview paper) that kinda combines hyperbolic and parabolic is:

, ,

where is the derivative at the fixed point 0, which is 1 in the parabolic case and you take the limit of lambda->1. I am in a hurry a bit. So perhaps more detailed later.

(07/21/2010, 10:41 PM)tommy1729 Wrote: im waiting and hoping for those " more details " dear bo.

Well, there is no more much to add, if you take the limit of the above right side:

you get if I not err, which is then the parabolic Levý formula.

If you could invert for then would be another formula for the hyperbolic Abel function.

If you can't (numerically/symbolically whatever) invert then you still have a different formula for the hyperbolic (and Lévy's formla for ) superfunction/iteration: