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+--- 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