Tagged Questions
3
votes
0answers
37 views
Order of Recursion?
Define an extended algebraic function f(a) as a function on a that utilizes any combination of recursive extensions and inversions of sequentiation. Example:
a + 1 = sequentiation. a + a = addition ...
5
votes
0answers
102 views
Notation for n-ary exponentiation
We have $n$-ary sums ($\sum$) and products ($\prod$). Is there an $n$-ary exponentiation operator?
$$\underset{i=1}{\overset{n}{\LARGE{\text{E}}}}\, x_i = x_1 \text{^} (x_2 \text{^} (\cdots \text{^} ...
4
votes
1answer
114 views
Operators - sums, products, exponents, etc.
$(x + x + \cdots + x)$, where $x$ added $n$ times can be written as $x * n$.
$(x * x * \cdots * x)$, where $x$ multiplied $n$ times can be written as $x ^ n$.
Is there an operator, such that if ...
21
votes
1answer
275 views
Iterated exponent of $i$
WolframAlpha seems to tell me that $e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^i}}}}}}}}}} = 1$, see link. Is this just an error or is it for real? Adding one more $e$ to the bottom of the tower gives me the ...
10
votes
1answer
263 views
Derivative of $x^{x^{\cdot^{\cdot}}}$?
The infinite tetration is defined as
$$f(x)=x^{x^{\cdot^{\cdot}}}$$
This function is defined for $e^{-e} \leq x \leq e^{e-1}$.
(Wikipedia image)
Can one determine the derivative of this function?
...
4
votes
1answer
180 views
Super logarithmic inverse of tetration
What's the super logarithmic inverse of tetration for $\bf{^{2}{x}}$?
Is it $slog^{x}_{2}$?
14
votes
1answer
551 views
Infinite tetration, convergence radius
I got this problem from my teacher as a optional challenge. I am open about this being a given problem, however it is not homework.
The problem is stated as follows. Assume we have an infinite ...
39
votes
4answers
2k views
Are the solutions of $x^{x^{x^{x^{\cdot^{{\cdot}^{\cdot}}}}}}=2$ correct?
Problem:
Find $x$ in
$$\large x^{x^{x^{x^{ \cdot^{{\cdot}^{\cdot}} }}}}=2$$
Trick:
$x^{x^{x^{x^{\cdot^{{\cdot}^{\cdot}}}}}}=2$, so,
$x^{(x^{x^{x^{\cdot^{{\cdot}^{\cdot}}}}})}=x^2=2$, and,
...
2
votes
0answers
158 views
What is the Equivalent Form of Tetration to the Exponential $n^{1/n}$?
I've been working on a project for a wiki that I'm a member of. It is the Sequence of the Day for September 2.
You can see my progress at ...
