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