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Inverse super-composition
#9
(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
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Messages In This Thread
Inverse super-composition - by Xorter - 11/24/2016, 12:53 PM
RE: Inverse super-composition - by JmsNxn - 11/25/2016, 08:55 PM
RE: Inverse super-composition - by Xorter - 12/23/2016, 01:33 PM
RE: Inverse super-composition - by JmsNxn - 12/23/2016, 08:12 PM
RE: Inverse super-composition - by Xorter - 12/24/2016, 09:53 PM
RE: Inverse super-composition - by sheldonison - 12/25/2016, 04:16 AM
RE: Inverse super-composition - by Xorter - 12/25/2016, 04:38 PM
RE: Inverse super-composition - by sheldonison - 12/25/2016, 08:35 PM
RE: Inverse super-composition - by Xorter - 12/25/2016, 10:23 PM
RE: Inverse super-composition - by sheldonison - 12/26/2016, 07:10 AM
RE: Inverse super-composition - by Xorter - 01/12/2017, 04:19 PM
RE: Inverse super-composition - by Xorter - 05/26/2018, 12:00 AM

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