Asymptotic behavior of the Mie-scattering amplitude

The asymptotic form of the Mie-scattering amplitude is of interest for a number of reasons, perhaps the most important of which is to reduce significantly the computational effort involved when the size parameter becomes large. Recently, Nussenzveig and Wiscombe [ Phys. Rev. Lett.45, 1490 ( 1980)] published an asymptotic expansion for the Mie extinction efficiency based on complex-angular-momentum theory. In this paper, we show how this result may be generalized to the full forward-scattering amplitude.