List questions from tetration

Published on 17 May 2016 - 8:46

201

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How to evaluate or approximate this kind of recursion: $a(n+1) = m \cdot \exp\left(\frac{-K \cdot (m - a(n))}{m}\right),\ n \geq 1$?

Published on 29 May 2016 - 12:08

197

Views

How can I show, that $N\uparrow\uparrow N$ is not "much larger" than $N$ for very large $N\ $?

Published on 25 Mar 2026 - 17:21

1.4k

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Does an iterated exponential $z^{z^{z^{...}}}$ always have a finite period

Published on 10 Jun 2016 - 0:46

545

Views

If $|t| = |W(-\ln z)| = 1$ and $t^n =1$ then $z^{z^{z^{...}}}$ is convergent

Published on 14 Jun 2016 - 20:21

119

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$e^{e^{10^{10^{2.8}}}}$ changing $e$ with $10$

Published on 23 Jun 2016 - 21:47

126

Views

Solve $(x+a)^{1/x} = b$ for $x$

Published on 30 Jun 2016 - 14:39

4.7k

Views

What is this operator called?

Published on 05 Jul 2016 - 8:42

201

Views

Limits of tetrations of infinite height

Published on 16 Apr 2013 - 5:16

973

Views

How do I calculate the 2nd term of continued fraction for the power tower ${^5}e=e^{e^{e^{e^{e}}}}$

Published on 25 Mar 2026 - 17:19

946

Views

Is the positive root of the equation $x^{x^x}=2$, $x=1.47668433...$ a transcendental number?

Published on 26 Mar 2026 - 3:13

462

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Is it possible to prove the positive root of the equation ${^4}x=2$, $x=1.4466014324...$ is irrational?

Published on 26 Mar 2026 - 11:01

308

Views

Tetration Binomial Theorem

Published on 01 May 2013 - 19:50

537

Views

Order of Recursion?

Published on 25 Mar 2026 - 17:17

2.1k

Views

Seems that I just proved $2=4$.

Published on 11 May 2013 - 12:42

List Question

Tetration of a number giving a complex number

How to evaluate or approximate this kind of recursion: $a(n+1) = m \cdot \exp\left(\frac{-K \cdot (m - a(n))}{m}\right),\ n \geq 1$?

How can I show, that $N\uparrow\uparrow N$ is not "much larger" than $N$ for very large $N\ $?

Does an iterated exponential $z^{z^{z^{...}}}$ always have a finite period

If $|t| = |W(-\ln z)| = 1$ and $t^n =1$ then $z^{z^{z^{...}}}$ is convergent

$e^{e^{10^{10^{2.8}}}}$ changing $e$ with $10$

Solve $(x+a)^{1/x} = b$ for $x$

What is this operator called?

Limits of tetrations of infinite height

How do I calculate the 2nd term of continued fraction for the power tower ${^5}e=e^{e^{e^{e^{e}}}}$

Is the positive root of the equation $x^{x^x}=2$, $x=1.47668433...$ a transcendental number?

Is it possible to prove the positive root of the equation ${^4}x=2$, $x=1.4466014324...$ is irrational?

Tetration Binomial Theorem

Order of Recursion?

Seems that I just proved $2=4$.

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