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.