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 fractional iteration by schröder and by binomial-formula Gottfried Ultimate Fellow Posts: 770 Threads: 120 Joined: Aug 2007 11/23/2011, 04:45 PM (This post was last modified: 11/23/2011, 04:49 PM by Gottfried.) Just a small result from some playing around in a break; I'll look at the confirmation for a wider range of parameters later. This days I'm re-considering the differences of the fractional iterates of $b^x -1$ using the schröder-function by their carleman-matrices. At the moment I use b=2, comparing the results when I use the power series centered around fixpoint t0=0 versus that around fixpoint t1=1. The range of 01. The point x0, at which the most symmetric sinusoidal curve occurs seems to be x0~0.382160520000... (not rational!) which has a special property for base b=2 which I'll discuss in a later post. Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

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