  Resonant States (RS), also known as Quasi-Normal Modes (QNMs), are
eigenstates that arise in spectral expansions of linear response functions of
open systems. Manipulation of these spatially `divergent' oscillating functions
requires a departure from the usual definitions of inner product, normalization
and orthogonality typically encountered in the studies of closed systems. We
show that once RS fields are expanded on a multipole basis, Gaussian
regularization methods provide \emph{analytical} results for crucial RS inner
product integrals \added{in the problematic region exterior to the scattering
system}. Our demonstrations are carried out in the context of light scattering
by spatially bounded objects composed of both electrically and magnetically
dispersive media, with demonstrative analytic calculations being shown to
\emph{completely} retrieve the results of exact Mie theory.
