4
$\begingroup$

A Tetration is defined as $${^{n}a} = \underbrace{a^{a^{\cdot^{\cdot^{a}}}}}_n$$ or, by a recursion function, $${^{n}a} := \begin{cases} 1 &\text{if }n=0 \\ a^{\left[^{(n-1)}a\right]} &\text{if }n>0 \end{cases} $$ That is, iterated exponentiation (like exponentiation is iterated multiplication). Exponentiation can be expressed as $e^{n\ln a}$ [1]

Is there a like way to express Tetrations? That is, a way to calculate for both negative and decimal Tetrations?

$\endgroup$

marked as duplicate by MJD, user147263, MathOverview, Micah, Ivo Terek Dec 1 '14 at 0:38

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

Browse other questions tagged or ask your own question.