How can one display the actual integral involved in special functions like this
MarcumQ[2, a, b]
in Mathematica?
?? MarcumQ
Then click on the >>
to go to the reference page. Then open the Details panel to see:
$Q_m(a,b) = \int\limits_b^\infty x \left( {x \over a}\right)^{m-1} I_{m-1}(a x) Exp[- {1 \over 2} (a^2 + x^2)]\ dx$
To get your Integral(s), You can use Wolfram|Alpha, see Wolfram|Alpha Integration, see also How can I get all the results from a Wolfram | Alpha query?,
You ca also use http://www.wolframalpha.com/