I was just wondering if there was any theory or theorems involving the convergence of a function's derivative/antiderivative taken an infinite number of times. It would seem to me that there are four types of ways that it can happen: it blows up to infinity, approaches zero, approaches some function, or alternates between several functions. Based on my premliminary investigations, there's even functions which do a combination of the three. Anyway, I'm basically looking for some reading material on the subject, and was hoping that one of you people have read something about it.(adsbygoogle = window.adsbygoogle || []).push({});

Furthermore, I'm looking for some reading material about techniques of evalutating/approximating integrals without a closed form, without using a sum of values in the interval as an approximation. Any help is vastly appreciated.

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# Infinite Differentiation and Integration?

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