f( f(x) ) = exp(x) solved ! ! !

[tommy1729]

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Well, because \( F(x) = w^x - 1 \) and \( G(x) = w^{x/w} = e^x \) are topologically conjugate (where \( w = -W(-1) \)), I kind of skipped a step and thought of F (which has a fixed point of 0) and G (which has a fixed point of w) at the same time.

Also, I do understand the general idea of tommy's method, to make a function with a fixed point at 0, as a limit of a function with a fixed point not at zero. It makes sense. I just need to sit down at look over the math for a week or so, to convince myself that it all works, and that it gives new insight to the problem.

Andrew Robbins
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ive been absent for a few days , but im thinking ( working ? ) on related ideas.

such as convergeance acceleration.

or a zero at other points then 0.

i dont think my fixed point at 0 gives a convex solution to tetration ...

i will post a conjecture soon.

regards

tommy1729