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

Abstract

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.