An analytic expression and an asymptotic estimate are derived for the definite integral of a product of Hermite functions (i.e., a Hermite polynomial times a Gaussian). The argument of each Hermite function is proportional but not neccesarily equal to the integration variable. The asymptotic estimate is used to show that the integral is negligible unless there are points where the sum of the local wave numbers is zero. This result is used, in the context of geophysical fluid dynamics, to establish a connection between the meridional interaction condition for equatorial waves, represented by Hermite functions, and midlatitude waves, represented by sinusoids: for the latter it is the sum of the constant wavenumbers that has to vanish.