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# Questions tagged [tetration]

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.

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### How to solve $ax^x+bx+c=0$?

How can I solve $$ax^x+bx+c=0$$ or $$ax^{x^x}+bx^x+cx+d=0$$ where $x^x$ and $x^{x^x}$ - tetration? Is there analogue of discriminant for it?
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### Tetration with 0 < #s < 1?

When I try numbers between 0 and 1 on my calculator app n-calc on my phone .. I get rapid convergence when the numbers are close to 1 .. And alternating but slow convergence when numbers are close to ...
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### function $\varphi$ such that $\varphi (\varphi (u))=\exp(u)$

Here it's cited: the existence of the holomorphic function $\varphi$ such that $\varphi (\varphi (u))=\exp(u)$ had been demonstrated in 1950 by Hellmuth Kneser. ...
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### Can tetration 'escape' the complex plane?

Considering subtraction can break out of the natural numbers and into integers, division can break out of integers and into rational numbers, and exponentiation can break out of rational numbers and ...
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### Solutions of $a^{a^x}=x$ for fixed $a>0$

I am interested in the equation $a^{a^x}=x$ for some fixed $a>0$. Is there some way to rearrange for $x$ or solve otherwise? What about the nature of the solutions? For which fixed $a>0$ are ...
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### How to solve 2 tetrated 0.5 times?

I've been really interested in tetration lately. So I came up with a seemingly simple problem to solve, which is 2 tetrated 0.5 times, which I'll write as the following. 2^^0.5 To make sense of this ...
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### Addition, Multiplication, Exponentiation, Tetration. Iterated functions.

Please note that I am exceptionally talented in over-complicating even the simplest of topics, however this may be worth a read. Also, the following operations are only performed with positive ...