# Asymptotic Approximation

1. May 7, 2013

### S_David

Hello all,

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

$$1-\prod_{m=1}^M(1-\rho^{-x_m})\doteq \sum_{m=1}^M \rho^{-x_m}$$

or

$$1-\prod_{m=1}^M(1-\rho^{-x_m})\doteq \rho^{-\underset{m}{\min}x_m}$$

Thanks

Last edited: May 7, 2013
2. May 7, 2013

### mathman

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.