# How to parse this formula?

1. Jun 3, 2015

### Jarvis323

I'm studying a research paper that gives this formula for the running time of an algorithm,

expO((log N)^α(log log N)^(1−α)) = L(a)

I would like to plot this function alongside another, for a = 1/4 + O(1), a = 1/4 + O(n), and a= 1/3. The function's growth parameratized by those a's, should be ordered from small to big in the order I listed them.

Here is a link to the article, the formula is found in the introduction.
The preprint (free) version of the article is http://arxiv.org/abs/1306.4244. Let $x= \log N$ and $y=\log\log N$. I parse that the argument of the exponent is $O(x^\alpha y^{1-\alpha})$.