  The Hermite-Gauss basis functions have been extensively employed in classical
and quantum optics due to their convenient analytic properties. A class of
multivariate Hermite-Gauss functions, the anisotropic Hermite-Gauss functions,
arise by endowing the standard univariate Hermite-Gauss functions with a
positive definite quadratic form. These multivariate functions admit useful
applications in optics, signal analysis and probability theory, however they
have received little attention in literature. In this paper, we examine the
properties of these functions, with an emphasis on applications in
computational optics.
