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 irrational iterate of 2z(1-z) tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 08/09/2014, 10:16 PM First Tommy-Ben Conjecture : let a,b,c be positive integers. Let X,Y be positive irrational numbers that are linearly independant but they are NOT algebraicly independant. Nomatter what X,Y are , there is NO non-Möbius closed form function f(x) such that f^[a + b X + c Y](x) is also a closed form for every a,b,c. --- Ben's OP was an example where f^[a + b X](x) had a closed form for every a,b. ( X was lb(3) ) Im very very convinced of this conjecture. --- Second Tommy-Ben conjecture : Let a_i be positive integers and X_i be linear independant positive irrational numbers. Let n be an integer > 0. If f^[a + a_1 X + a_2 X_2 + ... + a_n X_n](x) is a closed form for every a_i then the superfunction of f is a composition of at least 2 functions with an addition rule and the X_i are all of the form log(A_i)/log© where the A_i are integers and C is a constant. regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread irrational iterate of 2z(1-z) - by BenStandeven - 08/13/2010, 06:47 AM RE: irrational iterate of 2z(1-z) - by BenStandeven - 08/14/2010, 03:58 AM RE: irrational iterate of 2z(1-z) - by tommy1729 - 08/09/2014, 10:16 PM

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