A proper integral representation of Marcum Q-Function

A new proper integral representation of the first order Marcum Q-function Q(a, b) is derived and proved in this article. The most special feature of this form is that it holds the same representation for any value of arguments ratio a/b, meanwhile, it is can be used for stable numerical quadrature directly, and furthermore, it is also useful in the performance analysis of radar detection and digital communication systems analytically. The correctness of this new form is checked by the numerical comparison with the definition form of Marcum Q-function over a small and large domains in its two arguments.