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.)
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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
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I like anything to get an initial foothold! "Clarify to verify, try not to terrify" [Not sure why I put that in quotation marks; looks better that way...]
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Here’s my guess: crosses the x-axis at some x0, the y-axis at e^x0, and has a horizontal asymptote at y=x0.pic.twitter.com/pxnsWEck8q
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