12/25/2016, 10:23 PM

(12/25/2016, 08:35 PM)sheldonison Wrote: For a fixed point of zero, with a fixed point multiplier of 2, the general solution for the Abel function generated at the fixed point of zero is:

This is the Abel function for f(z)

where S(z) is the formal Schröder equation solution;

This is sometimes called Koenig's solution. It can be modified to work with any fixed point multiplier of k, |k|<>1. Using pari-gp one can easily write a program to generate the formal power series for S(x) given f(x).

I almost undestand it.

Okey, than what is the a[n] and b[n] in the sum formula?

I feel we are closer then ever before.

Could you show me this way with another example, please?

For instance, let us invastigate it: . (And cos' fixed point is ~0.739.) The question is that what N is and how I can calculate it.

Xorter Unizo