I wonder what a function f(x) with the property that f(f(x)) = e^x might look like. (My usual caveat: DON’T TELL ME & RUIN THE WONDERING STAGE.)
-
Maybe my question is naive{?} but: Does that boxed equation assume that f'(x) is well-defined i.e. that f is a differentiable function?
Indeed that is an unjustified assumption I am making, which I hope to--but am too lazy atm to-- "verify" by numerical plots
-
-
For f suitably nice - say, represented as a formal power series - then I think{?} one can write: f(x)=a_0 + a_1*x^1 + a_2*x^2 + ... then write down the power series for its self-composition and match coefficients with that of e^x i.e. all 1s. I don't think it's that nice, tho!
-
I agree that is where my head went too.. Being a physics guy myself, I'm more of the "try now verify later" camp.. sorry if that just made you sick
- 1 more reply
New conversation -
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.