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How to parse this formula?

  1. Jun 3, 2015 #1
    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.

    If you can help me interpret this in a way that I can plot the function correctly, that would be helpful.
  2. jcsd
  3. Jun 3, 2015 #2


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    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})##.
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