meromorphic idea

[tommy1729]

andydude wrote :

are there meromorphic functions f(x) so that they commute with exp(x) ?

I'm not sure if this is important, but I think what is important is whether or not:

"For all f(x) that satisfy \( f(\exp(x)) = \exp(f(x)) \), there exists a unique real number t such that \( f(x) = \exp^t(x) \)."

I'm not convinced that this is always true for holomorphic/meromorphic functions. I'm sure its false for for arbitrary (or piecewise-defined) functions. I also think this would be useful in characterizing fractional iterates.

Andrew Robbins

i kinda asked this question before - more or less -

see thread :

http://math.eretrandre.org/tetrationforu...hp?tid=270

yes , this is useful in characterizing fractional iterates.

and i believe it is important for some half-iterate questions , though i cant prove it to be for tetration , but im working on it.


regards

tommy1729