Integral involving Marcum Q-function

Asked May 02 '14 at 00:50

Active May 02 '14 at 03:22

Viewed 390 times

I'm struggling to find an approximation for the following integral:

$$\int\limits_0^\infty {{{\left[ {1 - Q\left( {a\sqrt t ,b} \right)} \right]}^n}{e^{ - t}}dt} $$

where ${Q\left( {a\sqrt t ,b} \right)}$ is the first order Marcum Q-function.

Do you have any idea how to do it? Thank you.

edited May 02 '14 at 03:22

Mhenni Benghorbal

asked May 02 '14 at 00:50

BinhDDT

Does this function come from statistics? – Mhenni Benghorbal May 02 '14 at 01:14
The function comes from a communication system performance analysis. – BinhDDT May 02 '14 at 01:28
You have not said anything about $n$! – Mhenni Benghorbal May 02 '14 at 01:30
n is greater than 2. – BinhDDT May 02 '14 at 01:31
@BBinh: approximation in what sense! – Mhenni Benghorbal May 02 '14 at 01:44
1

@MhenniBenghorbal: $a = \sqrt {\frac{{2\rho }}{{1 - \rho }}}$ and $b = \sqrt {\frac{{2{\gamma _0}}}{{\lambda \left( {1 - \rho } \right)}}}$.
($0 < \rho < 1$, and $\gamma_0$ is a constant). I want to find an approximation when $\lambda$ goes to infinity.
– BinhDDT May 02 '14 at 02:13
1

Does your $Q$ stands for $Q_1$? – Mhenni Benghorbal May 02 '14 at 04:33
Yes, it is. ^^^ – BinhDDT May 02 '14 at 06:58

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