As functions of $n$, $n^c$ is called power, and $e^n$ is called exponential. Is there a name for $n^n$ as a function of $n$? Thanks!
Added: consider the context of complexity of algorithms.
Also is $n^n$ an elementary function?
As functions of $n$, $n^c$ is called power, and $e^n$ is called exponential. Is there a name for $n^n$ as a function of $n$? Thanks!
Added: consider the context of complexity of algorithms.
Also is $n^n$ an elementary function?
This is also ${}^2n$, where the notation indicates the fourth hyper operator, which is most often called "tetration." Annoyingly, I don't know of any good way to read a tetration out loud-something like "$n$ tetrated twice" or "$n$ tetrate two", I suppose-or even "$n$ tetrated" as the special case of $n^n$.
But as I say, you'd have to explain yourself on any of these, so it's unlikely to be of any use, except maybe in the midst of a talk where you don't want to repeat "$n$ to the $n$" a dozen times. The hyper operators are mainly useful for simplifying notation of extraordinarily large numbers, so in day-to-day complexity theory they might not be of much use.
It doesn't have a commonly used name, no. You can call it a power tower of order 2 if you wish.