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
2answers
205 views
Uniqueness of Tetration
Let $f(0)=1$ and $f(x+1)=2^{f(x)}$
Also let f be infinitely differentiable. Then does f exist and is it unique?
If f is merely continuous, then any continuous function such that f(0)=1 f(1)=2 ...
7
votes
3answers
456 views
How to calculate $f(x)$ in $f(f(x)) = e^x$?
How would I calculate the power series of $f(x)$ if $f(f(x)) = e^x$? Is there a faster-converging method than power series for fractional iteration/functional square roots?
