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invariant ??
#1
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
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#2
(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 Smile
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#3
(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 Smile

Big Grin

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 Smile

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 ? Smile


regards

tommy1729
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