Can anyone point me to a proof?
An infinite tower of powers (also called tetration) converges only if x is in a special interval. Yes, that interval happens to be beautiful.pic.twitter.com/U0awOfOO3o
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The proof isn't too bad, i think. You first consider n tetrations and use e^ln(x) a bunch and then ask what the conditions are as n--> infinity
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I need
@3blue1brown to explain this to me -
Just wait til you see the region of convergence in the complex plane!
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I love that the two interval limits are the two different ways of parenthesizing of "e^e^(-1)"
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The statement in the picture should be converges not bounded.. Because x^x^.. is bounded in the interval (0,e^(1/e)] However, it does not converge in the interval (0, e^(-e) )
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Yup! Worked on some things with a professor here...good ol' Lambert-W function
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I learned about Lambert-W thanks to Hildebrand at UIUC. He made it a centerpiece in his asymptotic analysis class.
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Not surprised e is involved here...wasnt that guy trying to prove Riemann Zeta with these?
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