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Repeated Differentiation Leading to Tetrationally Fast Growth

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Repeated Differentiation Leading to Tetrationally Fast Growth
Daniel Offline
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07/13/2022, 08:43 AM
(07/13/2022, 02:45 AM)Catullus Wrote: Does anyone know of a function [Image: gif.image?\dpi%7B110%7Df(k)], such that the xth derivative of [Image: gif.image?\dpi%7B110%7Df(k)] grows tetrationally fast, for a fixed k?

First I should mention that the function you are looking for would be wildly divergent. While I don't know of any publication of such a function, it's construction would be straight forward.

For a given \( a\in\mathbb R \),
\( \sum_{n=0}^\infty ^na x^n \)
Daniel
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RE: Repeated Differentiation Leading to Tetrationally Fast Growth - by Daniel - 07/13/2022, 08:43 AM

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