conjecture 0 - 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: conjecture 0 (/showthread.php?tid=235) conjecture 0 - tommy1729 - 02/18/2009 any convex C oo solution for f(f(x)) = exp(x) is also an analytic solution for f(f(x)) = exp(x) RE: conjecture 0 - andydude - 02/18/2009 I suppose by "convex" you imply that the function is defined over the reals, and I suppose by "analytic" you mean real analytic. Is there an equivalent to "convex" for functions of a complex variable? Is this similar to requiring that a complex function be bounded over a strip of the complex plane? Andrew Robbins RE: conjecture 0 - tommy1729 - 02/18/2009 andydude Wrote:I suppose by "convex" you imply that the function is defined over the reals, and I suppose by "analytic" you mean real analytic. Is there an equivalent to "convex" for functions of a complex variable? Is this similar to requiring that a complex function be bounded over a strip of the complex plane? Andrew Robbins i do mean f(x) maps R to R yes. though convex is more than that of course. i assume " analytic " is false because of the fixpoint exp(x) = x ? real analytic makes a weaker conjecture ... and more likely to be true perhaps. as for your questions about 'convex for complex' i have no idea. regards tommy1729