• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 a vague idea for f(f(x)) = exp(x) tommy1729 Ultimate Fellow Posts: 1,438 Threads: 349 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 »

 Messages In This Thread a vague idea for f(f(x)) = exp(x) - by tommy1729 - 03/17/2009, 11:24 PM

 Possibly Related Threads... Thread Author Replies Views Last Post An intuitive idea log*^[n](F(exp*^[n](z0))) tommy1729 0 304 03/03/2021, 12:57 AM Last Post: tommy1729 (draft) integral idea tommy1729 0 3,459 06/25/2011, 10:17 PM Last Post: tommy1729 meromorphic idea tommy1729 2 6,581 05/13/2009, 11:18 PM Last Post: tommy1729 simple idea ... tommy1729 4 7,952 04/29/2009, 05:38 PM Last Post: bo198214 Uniqueness summary and idea bo198214 13 23,847 08/16/2007, 10:30 PM Last Post: jaydfox

Users browsing this thread: 1 Guest(s)