04/28/2009, 12:28 PM
a simple idea ... maybe considered before ?
let us approximate exp(x) with polynomials of degree n.
let us call that exp_n(x).
now we can solve for f_n(f_n(x)) = exp_n(x)
if n is large enough and then f_n(x) being a polynomial of degree < n.
( we ignore the terms of degree > n in f_n(f_n(x)) )
now if lim f_n(x) exists we got f(x) with f(f(x) = exp(x).
....
headscratch ...
regards
tommy1729
let us approximate exp(x) with polynomials of degree n.
let us call that exp_n(x).
now we can solve for f_n(f_n(x)) = exp_n(x)
if n is large enough and then f_n(x) being a polynomial of degree < n.
( we ignore the terms of degree > n in f_n(f_n(x)) )
now if lim f_n(x) exists we got f(x) with f(f(x) = exp(x).
....
headscratch ...
regards
tommy1729