a vague idea for f(f(x)) = exp(x) tommy1729 Ultimate Fellow Posts: 1,742 Threads: 382 Joined: Feb 2009 03/17/2009, 11:24 PM a vague idea ... f(f(x)) = exp(x) => f(f(x)) + O(x) * f(x) = exp(x) with O(x) approaching 0. => f_n-1(f_n-1(x)) - exp(x) = - f_n(x)/ n! => - n! * ( f_n-1(f_n-1(x)) - exp(x) ) = f_n(x) so starting at a suitable f_0(x) , whatever it may be , and applying the iteration : - n! * ( f_n-1(f_n-1(x)) - exp(x) ) = f_n(x) until it converges ( lim n -> oo ) at " f_oo(x) " ( convergeance depends upon f_0(x) of course ) if f_oo(x) is analytic , we have found f_oo(x) = f(x) with f(f(x)) =exp(x) !!!!!!!! i know : a vague idea. but perhaps promising. regards tommy1729 « Next Oldest | Next Newest »

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