Partial order generalized Marcum Q-function contour integral representation

A new contour integral representation of generalized Marcum Q-function is presented. The obtained expression is valid for an arbitrary positive order of the function and for a specific case of integer order yields a well known result. As an example of practical application the problem of energy base signal detection in presence of fading is considered. A novel closed form analytic expression for an average probability of detection for various channel models is obtained.