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Asymptotic Approximation

  1. May 7, 2013 #1
    Hello all,

    Which of the following asymptotic equations (as rho goes to infinity) correct:

    [tex]1-\prod_{m=1}^M(1-\rho^{-x_m})\doteq \sum_{m=1}^M \rho^{-x_m}[/tex]

    or

    [tex]1-\prod_{m=1}^M(1-\rho^{-x_m})\doteq \rho^{-\underset{m}{\min}x_m}[/tex]

    Thanks
     
    Last edited: May 7, 2013
  2. jcsd
  3. May 7, 2013 #2

    mathman

    User Avatar
    Science Advisor

    The first expression is more accurate. The second will do as long as the min xm appears only once. If it appears more than once, you need to multiply by the number of occurrences.
     
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