fractional iteration by schröder and by binomial-formula - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: fractional iteration by schröder and by binomial-formula (/showthread.php?tid=719) fractional iteration by schröder and by binomial-formula - Gottfried - 11/23/2011 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