Asymptotic Approximation

  • Thread starter EngWiPy
  • Start date
  • #1
1,367
61
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:

Answers and Replies

  • #2
mathman
Science Advisor
7,858
446
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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