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Results tagged with growth-rate
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user 454
6
votes
Accepted
The growth rate of $\left(1+\frac{x}{f(x)}\right)^{f(x)}$
Let's suppose $x/f(x) \to 0$. Then take logarithm. As $x \to \infty$,
$$
\log G(x) = f(x) \log\left(1+\frac{x}{f(x)}\right)
=f(x)\left(\frac{x}{f(x)}+O\left(\left(\frac{x}{f(x)}\right)^2\right)\righ …
- 41.1k
0
votes
Natural candidates for sub-half-exponential which limit to half-exponential function from below
Not an answer Merely remarks.
Let me use superscript $[k]$ for $k$-fold composition. $\log^{[3]} n$ means $\log\log\log n$.
As I remarked on the other question, for fixed $a$ and $n$, the value $f(k, …
- 41.1k