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Asymptotic and numerical aspects of the generalized Marcum function of the second kind

The asymptotic and numerical behavior of the so-called generalized Marcum
 function of the second kind is considered. By using some known expansions on
 the modified Bessel function of the second kind, we deduce the asymptotic
 expansions for the generalized Marcum function of the second kind for large
 parameters, and all the expansions are obtained when exactly one parameter
 is large and others are fixed. We also show numerically that the asymptotic
 formulas obtained in this paper are good approximations.