Tetration Forum
Conservation of functional equation ? - 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: Conservation of functional equation ? (/showthread.php?tid=996)



Conservation of functional equation ? - tommy1729 - 05/01/2015

Let f(x+1) = g(f(x)). With g real-entire.
What if the ROC around the point x is less than 1 , say 1/4 ?
Suppose we can get to the point x+1 by analytic continuation.
Does the equation still hold there ?
In case of "depends" , on what exactly does it depend ?
What are the classical examples of succes and failure ?

Regards

Tommy1729