functions - How to evaluate fractional tetrations? - Mathematics …
网页But in the case of tetration, there are no nice integral representations known. Henryk Trappmann and some others recently proved a theorem that gives a simple uniqueness criterion for the inverse of tetration (with respect to the "height") here, presuming extension not just to the real, but the complex numbers:
Is there an efficient implementation of tetration?
网页2016年12月8日 · With tetration, if the final answer is d digits, then all intermediate results are O(log d) digits, as opposed to O(d) digits with exponentiation. Because the intermediate results for tetration are so small compared to the final result, there's no savings to be had via divide and conquer.
real analysis - Infinite tetration, convergence radius - Mathematics ...
网页2016年4月14日 · My friend said you would have to treat the tetration as a infinite series, and therefore could not perform algebraic manipulations on it before it is know whether it converges or diverges. However my attempt is to first do some algebraic steps, then discuss the convergence radius.
Why are tetrations not useful? - Mathematics Stack Exchange
网页2021年11月6日 · I propose, when these two types of tetration are being discussed together, to use the term strong tetration for the ordinary notion of tetration and the term weak tetration for the ordinal notion of tetration as defined above. Top to Bottom Convention for Finite-Length and $\omega$-Length Towers of Exponentiation and Tetration.
soft question - Possible real extension of tetration, or ones with ...
网页2021年3月22日 · Counter-intuitively it appears that extending tetration to the complex numbers is easier than extending tetration to the real numbers. Likely because the complex numbers have more degrees of freedom. Special functions for extending tetration - Faà Di Bruno's formula and the Bell polynomials are invaluable in extending tetration.
calculus - $n^{th}$ derivative of a tetration function - Mathematics ...
网页2013年12月23日 · $\begingroup$ you are right that tetration is only a very special case (albeit the most interesting and tractable one) of iterated exponentiation. I have been playing with this idea for a while, and it was very satisfying to be able to crystallize my intuitions only a few days ago. basically all the integers $\gt 1$ can be formed from the ...
Newest 'tetration' Questions - Mathematics Stack Exchange
网页Tetration is iterated exponentiation, just as exponentiation is iterated multiplication. It is the fourth hyperoperation and often produces power towers that evaluate to very large numbers. Learn more…
Can tetration 'escape' the complex plane? - Mathematics Stack …
网页2017年11月4日 · Kneser's tetration solution and its inverse, the Slog are both analytic functions with Taylor series, and with singularities. In particular, Kneser's Tetration base(a) $\forall a>\exp(1/e)$ is analytic in the upper and lower halves of the complex plane, and at the real axis except for singularities at the integers <=-2.
What comes after tetration ? And after ? And after ? etc.
网页Tetration; What comes after tetration? What comes whatever comes after tetration? Is this generalized and easily understandale for non-mathematician? Note: I'm aware of this question, but it doesn't go deeper. I'm asking about the generalization of this process. Side question: We know that. 2 + 2 = 4 2 * 2 = 4 2 ^ 2 = 4 Is 2 <sign> 2 always 4?
Taylor series for tetration - Mathematics Stack Exchange
网页2017年12月8日 · $\begingroup$ I know it's a long time now, but I happened to be looking up the very same question. I couldn't help being amused by your little admonishon - yes it is a very frustrating subject all this hyperoperations business; and one gets the distinct impression that the series of mathematical operations defined recursively as the previous …