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Mizugadro, pentation, Book
#15
Ok I understand now.

But I fear I have to tell you your construction is not new.

It's just a classical fixpoint method used on an nonstandard function.

Your claim that it does not depend on M is thereby true and easy to prove.

To give a big hint :

suppose an analytic function f has a fixpoint at 0 with f ' (0) = Y > 1.

THEN for any real k , as n goes to oo :

pent(z) = sexp^[z](x_0) = f^[n] ( Y^(z-k) slog^[n+k](x_0) ).

Or said differently for any distinct pair reals k_1,k_2 :

f^[n] ( Y^(z-k_1) slog^[n+k_1](x_0) ) = f^[n] ( Y^(z-k_2) slog^[n+k_2](x_0) ).

At least if both sides converge.

Once you can see that , you will understand.

SECOND HINT : plug in koenigs function.

***

For those who can still follow , the real question is what if sexp(x-t) = x is a parabolic fixpoint ? Then how do we get GOOD convergeance for sexp(x-t)^[z].
Maybe thats not so hard either , but it seems a logical followup question.

***

---
Again for those who still follow , My answer is illuminating but the convergeance speedup is not yet understood.

---

I wonder about Eremenko's Conjecture regarding pentation.
I rediscovered Eremenko's Conjecture as a kid , guess that explains it.

regards

tommy1729
Reply


Messages In This Thread
Mizugadro, pentation, Book - by Kouznetsov - 01/11/2015, 06:05 AM
RE: Mizugadro, pentation, Book - by MphLee - 01/11/2015, 02:32 PM
RE: Mizugadro, pentation, Book - by Kouznetsov - 01/11/2015, 05:01 PM
RE: Mizugadro, pentation, Book - by tommy1729 - 01/12/2015, 12:06 AM
RE: Mizugadro, pentation, Book - by Kouznetsov - 01/12/2015, 05:11 AM
RE: Mizugadro, pentation, Book - by sheldonison - 01/13/2015, 02:56 PM
RE: Mizugadro, pentation, Book - by Kouznetsov - 01/13/2015, 06:52 PM
RE: Mizugadro, pentation, Book - by sheldonison - 01/13/2015, 09:02 PM
RE: Mizugadro, pentation, Book - by Kouznetsov - 01/14/2015, 01:12 AM
RE: Mizugadro, pentation, Book - by sheldonison - 01/12/2015, 03:43 AM
RE: Mizugadro, pentation, Book - by tommy1729 - 01/14/2015, 01:21 AM
RE: Mizugadro, pentation, Book - by Kouznetsov - 01/14/2015, 04:08 AM
RE: Mizugadro, pentation, Book - by tommy1729 - 01/15/2015, 01:12 PM
RE: Mizugadro, pentation, Book - by Kouznetsov - 01/15/2015, 03:09 PM
RE: Mizugadro, pentation, Book - by tommy1729 - 01/16/2015, 12:31 AM
RE: Mizugadro, pentation, Book - by MphLee - 02/09/2015, 08:19 PM
RE: Mizugadro, pentation, Book - by Kouznetsov - 02/10/2015, 12:07 AM
RE: Mizugadro, pentation, Book - by Kouznetsov - 02/10/2015, 12:18 AM
RE: Mizugadro, pentation, Book - by tommy1729 - 02/09/2015, 10:35 PM
RE: Mizugadro, pentation, Book - by MphLee - 02/10/2015, 12:48 PM
RE: Mizugadro, pentation, Book - by MphLee - 02/10/2015, 12:12 PM
RE: Mizugadro, pentation, Book - by Kouznetsov - 02/10/2015, 02:40 PM
RE: Mizugadro, pentation, Book - by Gottfried - 02/11/2015, 09:04 PM
RE: Mizugadro, pentation, Book - by Kouznetsov - 02/12/2015, 12:27 AM
RE: Mizugadro, pentation, Book - by Gottfried - 02/12/2015, 04:10 PM
RE: Mizugadro, pentation, Book - by Kouznetsov - 02/13/2015, 02:04 AM
RE: Mizugadro, pentation, Book - by Gottfried - 02/13/2015, 10:09 AM
RE: Mizugadro, pentation, Book - by Kouznetsov - 02/13/2015, 12:23 PM
RE: Mizugadro, pentation, Book - by tommy1729 - 02/13/2015, 12:45 AM
RE: Mizugadro, pentation, Book - by Kouznetsov - 02/13/2015, 02:25 AM
RE: Mizugadro, pentation, Book - by tommy1729 - 02/13/2015, 01:21 PM
RE: Mizugadro, pentation, Book - by Kouznetsov - 02/14/2015, 01:22 AM
RE: Mizugadro, pentation, Book - by tommy1729 - 02/15/2015, 05:23 PM
RE: Mizugadro, pentation, Book - by Kouznetsov - 02/16/2015, 12:03 AM
RE: Mizugadro, pentation, Book - by mike3 - 02/16/2015, 12:16 AM
RE: Mizugadro, pentation, Book - by tommy1729 - 02/16/2015, 01:05 AM
RE: Mizugadro, pentation, Book - by Kouznetsov - 02/16/2015, 01:47 AM
RE: Mizugadro, pentation, Book - by tommy1729 - 02/16/2015, 01:56 AM
RE: Mizugadro, pentation, Book - by tommy1729 - 02/16/2015, 02:23 AM
RE: Mizugadro, pentation, Book - by tommy1729 - 02/17/2015, 01:34 PM
RE: Mizugadro, pentation, Book - by MphLee - 02/17/2015, 03:36 PM
RE: Mizugadro, pentation, Book - by sheldonison - 03/02/2015, 08:13 PM

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