 invariant ?? - 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: invariant ?? (/showthread.php?tid=304) invariant ?? - tommy1729 - 06/12/2009 if F(g(x)) = F(x) for all x. and f(f(x)) = F(x) then f(g(x)) = f(x) for all x ?!? half - exp (x) = half - exp (x + 2pi i ) ?!? regards tommy1729 RE: invariant ?? - bo198214 - 06/14/2009 (06/12/2009, 12:30 PM)tommy1729 Wrote: if F(g(x)) = F(x) for all x. and f(f(x)) = F(x) then f(g(x)) = f(x) for all x ?!? half - exp (x) = half - exp (x + 2pi i ) ?!? yes RE: invariant ?? - tommy1729 - 06/14/2009 (06/14/2009, 04:23 PM)bo198214 Wrote: (06/12/2009, 12:30 PM)tommy1729 Wrote: if F(g(x)) = F(x) for all x. and f(f(x)) = F(x) then f(g(x)) = f(x) for all x ?!? half - exp (x) = half - exp (x + 2pi i ) ?!? yes  do all our known REAL solutions to f(f(x)) = exp(x) satisfy that* too ? ( * f(x) = f(x + 2pi i) ) in particular , does andrew robbins solution satisfy that ? regards tommy1729 ps : yes i like andrew robbins approach , sorry for the " discrimination " :p i love you all im currently considering andrew's solution as " the best " , however it might be equal to many many other people's solutions including my own. i think i can prove it , but im currently distracted with number theory research , so i wont go into detail ... i dont know if i will have much time for tetration in the nearby future , but i will keep reading this forum. im wondering , any other number theory freaks here ? regards tommy1729